Eigenvalue problems

This script explores how to use Matlab to solve eigenvalue problems. Both the naive and 'proper' way are shown.

Contents

The Eig function

The simplest way to compute eigenvalues and eigenvectors in Matlab is to use the built in "eig" function.

A=rand(10);
tic
EigVal1=eig(A)
toc

EigVal1 =

   4.7876 + 0.0000i
  -0.7449 + 0.3597i
  -0.7449 - 0.3597i
  -0.3286 + 0.4946i
  -0.3286 - 0.4946i
  -0.1755 + 0.5365i
  -0.1755 - 0.5365i
   0.1586 + 0.1528i
   0.1586 - 0.1528i
  -0.0319 + 0.0000i

Elapsed time is 0.000291 seconds.

This will produce a column vector of the eigenvalues of A. To also get the eigenvectors, return two outputs:

tic
[EigVec2,EigVal2]=eig(A);
toc

Elapsed time is 0.000281 seconds.

This will return the eigenvectors as the columns of EigVec, and the eigenvalues as the entries of the diagonal matrix EigVal.

Root Solving

We can also use Matlab to solve an eigenvalue problem in the direct way one would do it on paper. We can calculate the characteristic polynomial of our matrix and then find the roots. Using the built in functions charpoly and roots, this is:

tic
EigVal3=roots(charpoly(A))
toc

EigVal3 =

   4.7876 + 0.0000i
  -0.7449 + 0.3597i
  -0.7449 - 0.3597i
  -0.3286 + 0.4946i
  -0.3286 - 0.4946i
  -0.1755 + 0.5365i
  -0.1755 - 0.5365i
   0.1586 + 0.1528i
   0.1586 - 0.1528i
  -0.0319 + 0.0000i

Elapsed time is 0.097021 seconds.

Large matrices

As you can see in the timings, this method is significantly slower than using the built in function. For large enough matrices, it is not feasible to solve the problem algebraically.

A=rand(1000);
tic
EigVal4=eig(A)
toc
tic
[EigVec5,EigVal5]=eig(A);
toc

EigVal4 =

   1.0e+02 *

   5.0013 + 0.0000i
   0.0920 + 0.0148i
   0.0920 - 0.0148i
   0.0935 + 0.0000i
   0.0730 + 0.0548i
   0.0730 - 0.0548i
   0.0786 + 0.0463i
   0.0786 - 0.0463i
   0.0813 + 0.0393i
   0.0813 - 0.0393i
   0.0892 + 0.0000i
   0.0678 + 0.0598i
   0.0678 - 0.0598i
   0.0483 + 0.0785i
   0.0483 - 0.0785i
   0.0854 + 0.0247i
   0.0854 - 0.0247i
   0.0747 + 0.0480i
   0.0747 - 0.0480i
   0.0670 + 0.0581i
   0.0670 - 0.0581i
   0.0610 + 0.0642i
   0.0610 - 0.0642i
   0.0520 + 0.0722i
   0.0520 - 0.0722i
   0.0485 + 0.0747i
   0.0485 - 0.0747i
   0.0725 + 0.0480i
   0.0725 - 0.0480i
   0.0557 + 0.0672i
   0.0557 - 0.0672i
   0.0418 + 0.0784i
   0.0418 - 0.0784i
   0.0334 + 0.0825i
   0.0334 - 0.0825i
   0.0214 + 0.0870i
   0.0214 - 0.0870i
   0.0301 + 0.0829i
   0.0301 - 0.0829i
  -0.0050 + 0.0906i
  -0.0050 - 0.0906i
  -0.0430 + 0.0817i
  -0.0430 - 0.0817i
  -0.0340 + 0.0852i
  -0.0340 - 0.0852i
   0.0086 + 0.0880i
   0.0086 - 0.0880i
  -0.0301 + 0.0860i
  -0.0301 - 0.0860i
  -0.0914 + 0.0118i
  -0.0914 - 0.0118i
  -0.0472 + 0.0774i
  -0.0472 - 0.0774i
  -0.0646 + 0.0637i
  -0.0646 - 0.0637i
  -0.0906 + 0.0040i
  -0.0906 - 0.0040i
  -0.0896 + 0.0000i
  -0.0859 + 0.0293i
  -0.0859 - 0.0293i
  -0.0702 + 0.0570i
  -0.0702 - 0.0570i
  -0.0498 + 0.0744i
  -0.0498 - 0.0744i
  -0.0129 + 0.0879i
  -0.0129 - 0.0879i
  -0.0832 + 0.0346i
  -0.0832 - 0.0346i
  -0.0772 + 0.0449i
  -0.0772 - 0.0449i
  -0.0195 + 0.0866i
  -0.0195 - 0.0866i
  -0.0588 + 0.0657i
  -0.0588 - 0.0657i
  -0.0806 + 0.0370i
  -0.0806 - 0.0370i
  -0.0723 + 0.0500i
  -0.0723 - 0.0500i
  -0.0659 + 0.0570i
  -0.0659 - 0.0570i
  -0.0425 + 0.0765i
  -0.0425 - 0.0765i
  -0.0353 + 0.0805i
  -0.0353 - 0.0805i
  -0.0612 + 0.0611i
  -0.0612 - 0.0611i
   0.0854 + 0.0201i
   0.0854 - 0.0201i
   0.0869 + 0.0000i
   0.0854 + 0.0111i
   0.0854 - 0.0111i
   0.0600 + 0.0600i
   0.0600 - 0.0600i
   0.0502 + 0.0694i
   0.0502 - 0.0694i
   0.0390 + 0.0776i
   0.0390 - 0.0776i
   0.0145 + 0.0860i
   0.0145 - 0.0860i
  -0.0203 + 0.0851i
  -0.0203 - 0.0851i
   0.0291 + 0.0821i
   0.0291 - 0.0821i
  -0.0884 + 0.0059i
  -0.0884 - 0.0059i
  -0.0461 + 0.0721i
  -0.0461 - 0.0721i
  -0.0717 + 0.0477i
  -0.0717 - 0.0477i
  -0.0841 + 0.0240i
  -0.0841 - 0.0240i
  -0.0672 + 0.0531i
  -0.0672 - 0.0531i
   0.0775 + 0.0354i
   0.0775 - 0.0354i
  -0.0774 + 0.0378i
  -0.0774 - 0.0378i
   0.0808 + 0.0263i
   0.0808 - 0.0263i
   0.0655 + 0.0522i
   0.0655 - 0.0522i
   0.0602 + 0.0574i
   0.0602 - 0.0574i
  -0.0582 + 0.0606i
  -0.0582 - 0.0606i
  -0.0010 + 0.0856i
  -0.0010 - 0.0856i
   0.0092 + 0.0851i
   0.0092 - 0.0851i
  -0.0842 + 0.0176i
  -0.0842 - 0.0176i
  -0.0819 + 0.0262i
  -0.0819 - 0.0262i
  -0.0252 + 0.0813i
  -0.0252 - 0.0813i
  -0.0168 + 0.0838i
  -0.0168 - 0.0838i
   0.0674 + 0.0488i
   0.0674 - 0.0488i
   0.0833 + 0.0130i
   0.0833 - 0.0130i
   0.0025 + 0.0848i
   0.0025 - 0.0848i
  -0.0488 + 0.0670i
  -0.0488 - 0.0670i
   0.0788 + 0.0296i
   0.0788 - 0.0296i
   0.0759 + 0.0352i
   0.0759 - 0.0352i
   0.0811 + 0.0218i
   0.0811 - 0.0218i
   0.0411 + 0.0718i
   0.0411 - 0.0718i
   0.0518 + 0.0637i
   0.0518 - 0.0637i
  -0.0028 + 0.0841i
  -0.0028 - 0.0841i
   0.0831 + 0.0052i
   0.0831 - 0.0052i
   0.0448 + 0.0686i
   0.0448 - 0.0686i
   0.0532 + 0.0618i
   0.0532 - 0.0618i
   0.0596 + 0.0543i
   0.0596 - 0.0543i
  -0.0767 + 0.0324i
  -0.0767 - 0.0324i
  -0.0689 + 0.0455i
  -0.0689 - 0.0455i
  -0.0642 + 0.0504i
  -0.0642 - 0.0504i
  -0.0457 + 0.0675i
  -0.0457 - 0.0675i
  -0.0305 + 0.0773i
  -0.0305 - 0.0773i
   0.0214 + 0.0808i
   0.0214 - 0.0808i
  -0.0082 + 0.0825i
  -0.0082 - 0.0825i
   0.0709 + 0.0399i
   0.0709 - 0.0399i
   0.0695 + 0.0424i
   0.0695 - 0.0424i
   0.0805 + 0.0175i
   0.0805 - 0.0175i
  -0.0839 + 0.0000i
  -0.0831 + 0.0106i
  -0.0831 - 0.0106i
  -0.0647 + 0.0478i
  -0.0647 - 0.0478i
  -0.0599 + 0.0527i
  -0.0599 - 0.0527i
  -0.0413 + 0.0703i
  -0.0413 - 0.0703i
  -0.0464 + 0.0651i
  -0.0464 - 0.0651i
  -0.0007 + 0.0826i
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   0.0264 + 0.0780i
   0.0264 - 0.0780i
   0.0391 + 0.0707i
   0.0391 - 0.0707i
  -0.0506 + 0.0607i
  -0.0506 - 0.0607i
   0.0181 + 0.0802i
   0.0181 - 0.0802i
   0.0818 + 0.0026i
   0.0818 - 0.0026i
   0.0525 + 0.0593i
   0.0525 - 0.0593i
   0.0604 + 0.0504i
   0.0604 - 0.0504i
   0.0061 + 0.0819i
   0.0061 - 0.0819i
  -0.0787 + 0.0227i
  -0.0787 - 0.0227i
  -0.0810 + 0.0000i
  -0.0232 + 0.0785i
  -0.0232 - 0.0785i
  -0.0489 + 0.0617i
  -0.0489 - 0.0617i
   0.0602 + 0.0495i
   0.0602 - 0.0495i
  -0.0820 + 0.0041i
  -0.0820 - 0.0041i
  -0.0574 + 0.0526i
  -0.0574 - 0.0526i
   0.0780 + 0.0193i
   0.0780 - 0.0193i
   0.0766 + 0.0244i
   0.0766 - 0.0244i
   0.0657 + 0.0427i
   0.0657 - 0.0427i
   0.0742 + 0.0284i
   0.0742 - 0.0284i
   0.0184 + 0.0788i
   0.0184 - 0.0788i
   0.0297 + 0.0741i
   0.0297 - 0.0741i
   0.0440 + 0.0643i
   0.0440 - 0.0643i
  -0.0141 + 0.0797i
  -0.0141 - 0.0797i
  -0.0349 + 0.0720i
  -0.0349 - 0.0720i
  -0.0197 + 0.0781i
  -0.0197 - 0.0781i
  -0.0379 + 0.0697i
  -0.0379 - 0.0697i
  -0.0032 + 0.0800i
  -0.0032 - 0.0800i
  -0.0688 + 0.0392i
  -0.0688 - 0.0392i
  -0.0791 + 0.0157i
  -0.0791 - 0.0157i
  -0.0537 + 0.0550i
  -0.0537 - 0.0550i
  -0.0747 + 0.0268i
  -0.0747 - 0.0268i
  -0.0653 + 0.0424i
  -0.0653 - 0.0424i
  -0.0705 + 0.0350i
  -0.0705 - 0.0350i
  -0.0767 + 0.0215i
  -0.0767 - 0.0215i
  -0.0670 + 0.0382i
  -0.0670 - 0.0382i
  -0.0785 + 0.0137i
  -0.0785 - 0.0137i
  -0.0708 + 0.0330i
  -0.0708 - 0.0330i
   0.0780 + 0.0127i
   0.0780 - 0.0127i
   0.0724 + 0.0315i
   0.0724 - 0.0315i
  -0.0074 + 0.0793i
  -0.0074 - 0.0793i
   0.0169 + 0.0774i
   0.0169 - 0.0774i
   0.0288 + 0.0735i
   0.0288 - 0.0735i
   0.0409 + 0.0644i
   0.0409 - 0.0644i
   0.0610 + 0.0450i
   0.0610 - 0.0450i
   0.0553 + 0.0514i
   0.0553 - 0.0514i
   0.0701 + 0.0343i
   0.0701 - 0.0343i
  -0.0494 + 0.0559i
  -0.0494 - 0.0559i
  -0.0722 + 0.0283i
  -0.0722 - 0.0283i
   0.0077 + 0.0781i
   0.0077 - 0.0781i
   0.0365 + 0.0683i
   0.0365 - 0.0683i
   0.0770 + 0.0033i
   0.0770 - 0.0033i
  -0.0009 + 0.0778i
  -0.0009 - 0.0778i
   0.0759 + 0.0128i
   0.0759 - 0.0128i
  -0.0276 + 0.0726i
  -0.0276 - 0.0726i
  -0.0130 + 0.0762i
  -0.0130 - 0.0762i
  -0.0614 + 0.0437i
  -0.0614 - 0.0437i
  -0.0782 + 0.0008i
  -0.0782 - 0.0008i
   0.0720 + 0.0257i
   0.0720 - 0.0257i
  -0.0291 + 0.0703i
  -0.0291 - 0.0703i
   0.0447 + 0.0593i
   0.0447 - 0.0593i
  -0.0441 + 0.0599i
  -0.0441 - 0.0599i
   0.0293 + 0.0701i
   0.0293 - 0.0701i
  -0.0748 + 0.0159i
  -0.0748 - 0.0159i
  -0.0249 + 0.0720i
  -0.0249 - 0.0720i
  -0.0756 + 0.0105i
  -0.0756 - 0.0105i
   0.0143 + 0.0749i
   0.0143 - 0.0749i
   0.0652 + 0.0358i
   0.0652 - 0.0358i
   0.0749 + 0.0111i
   0.0749 - 0.0111i
  -0.0361 + 0.0642i
  -0.0361 - 0.0642i
  -0.0208 + 0.0730i
  -0.0208 - 0.0730i
   0.0208 + 0.0726i
   0.0208 - 0.0726i
  -0.0159 + 0.0742i
  -0.0159 - 0.0742i
  -0.0491 + 0.0525i
  -0.0491 - 0.0525i
   0.0518 + 0.0502i
   0.0518 - 0.0502i
   0.0119 + 0.0742i
   0.0119 - 0.0742i
   0.0670 + 0.0302i
   0.0670 - 0.0302i
   0.0686 + 0.0257i
   0.0686 - 0.0257i
  -0.0302 + 0.0673i
  -0.0302 - 0.0673i
   0.0015 + 0.0742i
   0.0015 - 0.0742i
  -0.0713 + 0.0200i
  -0.0713 - 0.0200i
   0.0649 + 0.0331i
   0.0649 - 0.0331i
  -0.0362 + 0.0630i
  -0.0362 - 0.0630i
   0.0462 + 0.0542i
   0.0462 - 0.0542i
  -0.0713 + 0.0156i
  -0.0713 - 0.0156i
  -0.0645 + 0.0308i
  -0.0645 - 0.0308i
  -0.0725 + 0.0040i
  -0.0725 - 0.0040i
   0.0258 + 0.0690i
   0.0258 - 0.0690i
   0.0351 + 0.0637i
   0.0351 - 0.0637i
  -0.0524 + 0.0470i
  -0.0524 - 0.0470i
  -0.0546 + 0.0440i
  -0.0546 - 0.0440i
   0.0297 + 0.0657i
   0.0297 - 0.0657i
   0.0530 + 0.0468i
   0.0530 - 0.0468i
  -0.0276 + 0.0657i
  -0.0276 - 0.0657i
  -0.0203 + 0.0684i
  -0.0203 - 0.0684i
   0.0497 + 0.0494i
   0.0497 - 0.0494i
   0.0459 + 0.0530i
   0.0459 - 0.0530i
   0.0211 + 0.0686i
   0.0211 - 0.0686i
   0.0709 + 0.0098i
   0.0709 - 0.0098i
  -0.0087 + 0.0709i
  -0.0087 - 0.0709i
   0.0074 + 0.0708i
   0.0074 - 0.0708i
  -0.0350 + 0.0611i
  -0.0350 - 0.0611i
   0.0389 + 0.0580i
   0.0389 - 0.0580i
   0.0323 + 0.0624i
   0.0323 - 0.0624i
   0.0718 + 0.0053i
   0.0718 - 0.0053i
  -0.0709 + 0.0000i
  -0.0647 + 0.0278i
  -0.0647 - 0.0278i
  -0.0603 + 0.0345i
  -0.0603 - 0.0345i
  -0.0415 + 0.0551i
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  -0.0491 + 0.0470i
  -0.0491 - 0.0470i
  -0.0561 + 0.0392i
  -0.0561 - 0.0392i
  -0.0538 + 0.0419i
  -0.0538 - 0.0419i
   0.0030 + 0.0707i
   0.0030 - 0.0707i
   0.0135 + 0.0692i
   0.0135 - 0.0692i
   0.0565 + 0.0379i
   0.0565 - 0.0379i
   0.0706 + 0.0061i
   0.0706 - 0.0061i
   0.0679 + 0.0199i
   0.0679 - 0.0199i
  -0.0659 + 0.0216i
  -0.0659 - 0.0216i
  -0.0007 + 0.0698i
  -0.0007 - 0.0698i
   0.0663 + 0.0203i
   0.0663 - 0.0203i
   0.0356 + 0.0582i
   0.0356 - 0.0582i
   0.0672 + 0.0153i
   0.0672 - 0.0153i
   0.0585 + 0.0349i
   0.0585 - 0.0349i
   0.0229 + 0.0649i
   0.0229 - 0.0649i
  -0.0667 + 0.0154i
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   0.0541 + 0.0389i
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  -0.0676 + 0.0000i
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   0.0666 + 0.0047i
   0.0666 - 0.0047i
   0.0193 + 0.0645i
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   0.0353 + 0.0550i
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  -0.0126 + 0.0674i
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  -0.0238 + 0.0618i
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   0.0516 - 0.0357i
   0.0610 + 0.0219i
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  -0.0036 + 0.0653i
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   0.0275 + 0.0581i
   0.0275 - 0.0581i
   0.0583 + 0.0256i
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   0.0051 + 0.0645i
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   0.0645 + 0.0072i
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  -0.0591 - 0.0145i
   0.0234 + 0.0564i
   0.0234 - 0.0564i
   0.0474 + 0.0353i
   0.0474 - 0.0353i
   0.0416 + 0.0408i
   0.0416 - 0.0408i
  -0.0387 + 0.0441i
  -0.0387 - 0.0441i
  -0.0068 + 0.0605i
  -0.0068 - 0.0605i
  -0.0603 + 0.0058i
  -0.0603 - 0.0058i
   0.0347 + 0.0471i
   0.0347 - 0.0471i
   0.0552 + 0.0239i
   0.0552 - 0.0239i
   0.0400 + 0.0416i
   0.0400 - 0.0416i
   0.0607 + 0.0000i
  -0.0527 + 0.0267i
  -0.0527 - 0.0267i
   0.0182 + 0.0566i
   0.0182 - 0.0566i
   0.0597 + 0.0071i
   0.0597 - 0.0071i
  -0.0577 + 0.0141i
  -0.0577 - 0.0141i
  -0.0499 + 0.0302i
  -0.0499 - 0.0302i
  -0.0593 + 0.0000i
  -0.0579 + 0.0085i
  -0.0579 - 0.0085i
   0.0125 + 0.0574i
   0.0125 - 0.0574i
  -0.0527 + 0.0210i
  -0.0527 - 0.0210i
  -0.0035 + 0.0587i
  -0.0035 - 0.0587i
  -0.0452 + 0.0336i
  -0.0452 - 0.0336i
   0.0574 + 0.0139i
   0.0574 - 0.0139i
  -0.0214 + 0.0529i
  -0.0214 - 0.0529i
  -0.0399 + 0.0384i
  -0.0399 - 0.0384i
   0.0071 + 0.0576i
   0.0071 - 0.0576i
   0.0556 + 0.0178i
   0.0556 - 0.0178i
  -0.0574 + 0.0000i
   0.0475 + 0.0302i
   0.0475 - 0.0302i
   0.0236 + 0.0519i
   0.0236 - 0.0519i
  -0.0223 + 0.0506i
  -0.0223 - 0.0506i
  -0.0140 + 0.0539i
  -0.0140 - 0.0539i
   0.0179 + 0.0539i
   0.0179 - 0.0539i
   0.0506 + 0.0247i
   0.0506 - 0.0247i
  -0.0021 + 0.0564i
  -0.0021 - 0.0564i
   0.0539 + 0.0181i
   0.0539 - 0.0181i
  -0.0541 + 0.0131i
  -0.0541 - 0.0131i
   0.0263 + 0.0485i
   0.0263 - 0.0485i
   0.0302 + 0.0449i
   0.0302 - 0.0449i
   0.0562 + 0.0000i
   0.0410 + 0.0347i
   0.0410 - 0.0347i
  -0.0111 + 0.0533i
  -0.0111 - 0.0533i
  -0.0379 + 0.0374i
  -0.0379 - 0.0374i
   0.0026 + 0.0546i
   0.0026 - 0.0546i
  -0.0473 + 0.0252i
  -0.0473 - 0.0252i
  -0.0501 + 0.0191i
  -0.0501 - 0.0191i
   0.0538 + 0.0000i
   0.0423 + 0.0305i
   0.0423 - 0.0305i
   0.0131 + 0.0530i
   0.0131 - 0.0530i
  -0.0553 + 0.0026i
  -0.0553 - 0.0026i
  -0.0219 + 0.0488i
  -0.0219 - 0.0488i
   0.0057 + 0.0535i
   0.0057 - 0.0535i
  -0.0229 + 0.0470i
  -0.0229 - 0.0470i
  -0.0385 + 0.0348i
  -0.0385 - 0.0348i
  -0.0408 + 0.0320i
  -0.0408 - 0.0320i
  -0.0275 + 0.0440i
  -0.0275 - 0.0440i
   0.0525 + 0.0112i
   0.0525 - 0.0112i
   0.0531 + 0.0068i
   0.0531 - 0.0068i
  -0.0336 + 0.0379i
  -0.0336 - 0.0379i
   0.0328 + 0.0383i
   0.0328 - 0.0383i
  -0.0185 + 0.0494i
  -0.0185 - 0.0494i
   0.0121 + 0.0517i
   0.0121 - 0.0517i
   0.0364 + 0.0336i
   0.0364 - 0.0336i
   0.0404 + 0.0286i
   0.0404 - 0.0286i
  -0.0042 + 0.0526i
  -0.0042 - 0.0526i
  -0.0520 + 0.0077i
  -0.0520 - 0.0077i
  -0.0104 + 0.0506i
  -0.0104 - 0.0506i
  -0.0083 + 0.0504i
  -0.0083 - 0.0504i
   0.0022 + 0.0512i
   0.0022 - 0.0512i
  -0.0465 + 0.0195i
  -0.0465 - 0.0195i
   0.0080 + 0.0507i
   0.0080 - 0.0507i
   0.0227 + 0.0454i
   0.0227 - 0.0454i
  -0.0499 + 0.0077i
  -0.0499 - 0.0077i
   0.0244 + 0.0441i
   0.0244 - 0.0441i
  -0.0405 + 0.0276i
  -0.0405 - 0.0276i
  -0.0292 + 0.0397i
  -0.0292 - 0.0397i
   0.0483 + 0.0184i
   0.0483 - 0.0184i
   0.0442 + 0.0246i
   0.0442 - 0.0246i
  -0.0192 + 0.0452i
  -0.0192 - 0.0452i
   0.0165 + 0.0465i
   0.0165 - 0.0465i
  -0.0411 + 0.0244i
  -0.0411 - 0.0244i
   0.0476 + 0.0153i
   0.0476 - 0.0153i
   0.0461 + 0.0181i
   0.0461 - 0.0181i
   0.0497 + 0.0051i
   0.0497 - 0.0051i
  -0.0309 + 0.0356i
  -0.0309 - 0.0356i
  -0.0253 + 0.0401i
  -0.0253 - 0.0401i
   0.0375 + 0.0291i
   0.0375 - 0.0291i
   0.0407 + 0.0241i
   0.0407 - 0.0241i
   0.0346 + 0.0310i
   0.0346 - 0.0310i
  -0.0227 + 0.0403i
  -0.0227 - 0.0403i
   0.0310 + 0.0336i
   0.0310 - 0.0336i
  -0.0484 + 0.0000i
   0.0322 + 0.0317i
   0.0322 - 0.0317i
  -0.0466 + 0.0132i
  -0.0466 - 0.0132i
  -0.0376 + 0.0253i
  -0.0376 - 0.0253i
   0.0182 + 0.0431i
   0.0182 - 0.0431i
   0.0148 + 0.0443i
   0.0148 - 0.0443i
   0.0470 + 0.0037i
   0.0470 - 0.0037i
  -0.0471 + 0.0072i
  -0.0471 - 0.0072i
  -0.0442 + 0.0153i
  -0.0442 - 0.0153i
  -0.0070 + 0.0457i
  -0.0070 - 0.0457i
  -0.0465 + 0.0029i
  -0.0465 - 0.0029i
   0.0067 + 0.0458i
   0.0067 - 0.0458i
  -0.0275 + 0.0351i
  -0.0275 - 0.0351i
   0.0011 + 0.0450i
   0.0011 - 0.0450i
  -0.0140 + 0.0421i
  -0.0140 - 0.0421i
   0.0250 + 0.0372i
   0.0250 - 0.0372i
   0.0449 + 0.0115i
   0.0449 - 0.0115i
  -0.0110 + 0.0427i
  -0.0110 - 0.0427i
  -0.0339 + 0.0275i
  -0.0339 - 0.0275i
   0.0412 + 0.0168i
   0.0412 - 0.0168i
   0.0196 + 0.0391i
   0.0196 - 0.0391i
   0.0436 + 0.0105i
   0.0436 - 0.0105i
   0.0448 + 0.0058i
   0.0448 - 0.0058i
  -0.0415 + 0.0140i
  -0.0415 - 0.0140i
  -0.0217 + 0.0361i
  -0.0217 - 0.0361i
   0.0045 + 0.0422i
   0.0045 - 0.0422i
  -0.0432 + 0.0000i
   0.0445 + 0.0019i
   0.0445 - 0.0019i
   0.0211 + 0.0358i
   0.0211 - 0.0358i
   0.0359 + 0.0192i
   0.0359 - 0.0192i
  -0.0291 + 0.0286i
  -0.0291 - 0.0286i
  -0.0378 + 0.0172i
  -0.0378 - 0.0172i
   0.0274 + 0.0296i
   0.0274 - 0.0296i
   0.0239 + 0.0322i
   0.0239 - 0.0322i
  -0.0023 + 0.0419i
  -0.0023 - 0.0419i
  -0.0360 + 0.0194i
  -0.0360 - 0.0194i
   0.0373 + 0.0153i
   0.0373 - 0.0153i
  -0.0093 + 0.0400i
  -0.0093 - 0.0400i
   0.0316 + 0.0217i
   0.0316 - 0.0217i
  -0.0418 + 0.0000i
   0.0396 + 0.0094i
   0.0396 - 0.0094i
   0.0137 + 0.0369i
   0.0137 - 0.0369i
  -0.0322 + 0.0204i
  -0.0322 - 0.0204i
   0.0286 + 0.0241i
   0.0286 - 0.0241i
  -0.0135 + 0.0368i
  -0.0135 - 0.0368i
  -0.0012 + 0.0396i
  -0.0012 - 0.0396i
  -0.0236 + 0.0275i
  -0.0236 - 0.0275i
  -0.0394 + 0.0061i
  -0.0394 - 0.0061i
   0.0391 + 0.0042i
   0.0391 - 0.0042i
   0.0082 + 0.0376i
   0.0082 - 0.0376i
   0.0187 + 0.0307i
   0.0187 - 0.0307i
   0.0273 + 0.0229i
   0.0273 - 0.0229i
   0.0236 + 0.0260i
   0.0236 - 0.0260i
   0.0335 + 0.0088i
   0.0335 - 0.0088i
   0.0035 + 0.0363i
   0.0035 - 0.0363i
   0.0103 + 0.0339i
   0.0103 - 0.0339i
   0.0310 + 0.0131i
   0.0310 - 0.0131i
  -0.0129 + 0.0341i
  -0.0129 - 0.0341i
  -0.0180 + 0.0309i
  -0.0180 - 0.0309i
  -0.0357 + 0.0115i
  -0.0357 - 0.0115i
  -0.0028 + 0.0346i
  -0.0028 - 0.0346i
  -0.0338 + 0.0143i
  -0.0338 - 0.0143i
  -0.0276 + 0.0222i
  -0.0276 - 0.0222i
  -0.0097 + 0.0324i
  -0.0097 - 0.0324i
  -0.0352 + 0.0080i
  -0.0352 - 0.0080i
  -0.0185 + 0.0268i
  -0.0185 - 0.0268i
  -0.0348 + 0.0026i
  -0.0348 - 0.0026i
  -0.0141 + 0.0287i
  -0.0141 - 0.0287i
  -0.0285 + 0.0155i
  -0.0285 - 0.0155i
  -0.0222 + 0.0221i
  -0.0222 - 0.0221i
  -0.0334 + 0.0010i
  -0.0334 - 0.0010i
   0.0032 + 0.0323i
   0.0032 - 0.0323i
   0.0337 + 0.0034i
   0.0337 - 0.0034i
   0.0145 + 0.0273i
   0.0145 - 0.0273i
   0.0264 + 0.0159i
   0.0264 - 0.0159i
   0.0077 + 0.0287i
   0.0077 - 0.0287i
  -0.0042 + 0.0302i
  -0.0042 - 0.0302i
  -0.0096 + 0.0277i
  -0.0096 - 0.0277i
  -0.0246 + 0.0154i
  -0.0246 - 0.0154i
  -0.0310 + 0.0029i
  -0.0310 - 0.0029i
  -0.0208 + 0.0195i
  -0.0208 - 0.0195i
  -0.0176 + 0.0227i
  -0.0176 - 0.0227i
  -0.0297 + 0.0052i
  -0.0297 - 0.0052i
   0.0136 + 0.0258i
   0.0136 - 0.0258i
   0.0236 + 0.0167i
   0.0236 - 0.0167i
   0.0285 + 0.0089i
   0.0285 - 0.0089i
  -0.0001 + 0.0292i
  -0.0001 - 0.0292i
   0.0181 + 0.0204i
   0.0181 - 0.0204i
   0.0292 + 0.0000i
  -0.0119 + 0.0241i
  -0.0119 - 0.0241i
  -0.0204 + 0.0145i
  -0.0204 - 0.0145i
   0.0197 + 0.0153i
   0.0197 - 0.0153i
   0.0258 + 0.0084i
   0.0258 - 0.0084i
  -0.0029 + 0.0268i
  -0.0029 - 0.0268i
   0.0289 + 0.0000i
  -0.0256 + 0.0059i
  -0.0256 - 0.0059i
   0.0273 + 0.0020i
   0.0273 - 0.0020i
   0.0096 + 0.0239i
   0.0096 - 0.0239i
  -0.0244 + 0.0000i
  -0.0237 + 0.0061i
  -0.0237 - 0.0061i
   0.0173 + 0.0169i
   0.0173 - 0.0169i
  -0.0234 + 0.0000i
  -0.0190 + 0.0119i
  -0.0190 - 0.0119i
  -0.0113 + 0.0196i
  -0.0113 - 0.0196i
  -0.0010 + 0.0231i
  -0.0010 - 0.0231i
   0.0065 + 0.0230i
   0.0065 - 0.0230i
   0.0206 + 0.0102i
   0.0206 - 0.0102i
  -0.0049 + 0.0216i
  -0.0049 - 0.0216i
  -0.0135 + 0.0162i
  -0.0135 - 0.0162i
   0.0070 + 0.0212i
   0.0070 - 0.0212i
   0.0113 + 0.0184i
   0.0113 - 0.0184i
   0.0076 + 0.0205i
   0.0076 - 0.0205i
   0.0216 + 0.0058i
   0.0216 - 0.0058i
  -0.0182 + 0.0076i
  -0.0182 - 0.0076i
  -0.0102 + 0.0155i
  -0.0102 - 0.0155i
   0.0182 + 0.0074i
   0.0182 - 0.0074i
  -0.0017 + 0.0170i
  -0.0017 - 0.0170i
   0.0213 + 0.0000i
   0.0194 + 0.0000i
   0.0178 + 0.0000i
  -0.0131 + 0.0086i
  -0.0131 - 0.0086i
  -0.0104 + 0.0103i
  -0.0104 - 0.0103i
   0.0064 + 0.0139i
   0.0064 - 0.0139i
   0.0086 + 0.0132i
   0.0086 - 0.0132i
  -0.0138 + 0.0034i
  -0.0138 - 0.0034i
  -0.0011 + 0.0140i
  -0.0011 - 0.0140i
   0.0114 + 0.0075i
   0.0114 - 0.0075i
  -0.0087 + 0.0084i
  -0.0087 - 0.0084i
   0.0105 + 0.0016i
   0.0105 - 0.0016i
  -0.0128 + 0.0008i
  -0.0128 - 0.0008i
   0.0097 + 0.0085i
   0.0097 - 0.0085i
  -0.0032 + 0.0092i
  -0.0032 - 0.0092i
   0.0035 + 0.0086i
   0.0035 - 0.0086i
   0.0090 + 0.0040i
   0.0090 - 0.0040i
   0.0001 + 0.0085i
   0.0001 - 0.0085i
  -0.0078 + 0.0015i
  -0.0078 - 0.0015i
   0.0065 + 0.0000i
  -0.0043 + 0.0000i
  -0.0004 + 0.0000i
   0.0010 + 0.0000i

Elapsed time is 0.845069 seconds.
Elapsed time is 1.303864 seconds.

If the matrix you are considering is very large, you may not want all of the eigenvalues, in this case you can use:

tic
EigVal6=eigs(A);
toc

Elapsed time is 1.893703 seconds.

This returns the largest (in magnitude) six eigenvalues of the matrix. The function works the same as the previous one to calculate eigenvectors.

tic
[EigVec7,EigVal7]=eigs(A)
toc

EigVec7 =

  Columns 1 through 4

   0.0328 + 0.0000i   0.0276 + 0.0000i  -0.0043 + 0.0225i  -0.0043 - 0.0225i
   0.0315 + 0.0000i  -0.0363 + 0.0000i  -0.0451 - 0.0011i  -0.0451 + 0.0011i
   0.0329 + 0.0000i  -0.0009 + 0.0000i   0.0071 + 0.0204i   0.0071 - 0.0204i
   0.0298 + 0.0000i   0.0055 + 0.0000i  -0.0104 - 0.0227i  -0.0104 + 0.0227i
   0.0306 + 0.0000i  -0.0317 + 0.0000i   0.0014 + 0.0340i   0.0014 - 0.0340i
   0.0311 + 0.0000i   0.0049 + 0.0000i   0.0071 - 0.0165i   0.0071 + 0.0165i
   0.0309 + 0.0000i   0.0796 + 0.0000i   0.0025 - 0.0272i   0.0025 + 0.0272i
   0.0321 + 0.0000i  -0.0498 + 0.0000i   0.0381 - 0.0321i   0.0381 + 0.0321i
   0.0315 + 0.0000i  -0.0527 + 0.0000i   0.0156 + 0.0025i   0.0156 - 0.0025i
   0.0312 + 0.0000i   0.0053 + 0.0000i  -0.0098 + 0.0099i  -0.0098 - 0.0099i
   0.0314 + 0.0000i   0.0302 + 0.0000i   0.0427 + 0.0158i   0.0427 - 0.0158i
   0.0325 + 0.0000i   0.0309 + 0.0000i   0.0529 + 0.0079i   0.0529 - 0.0079i
   0.0319 + 0.0000i   0.0207 + 0.0000i   0.0546 - 0.0217i   0.0546 + 0.0217i
   0.0309 + 0.0000i   0.0538 + 0.0000i   0.0053 - 0.0180i   0.0053 + 0.0180i
   0.0316 + 0.0000i   0.0096 + 0.0000i  -0.0104 - 0.0117i  -0.0104 + 0.0117i
   0.0317 + 0.0000i   0.0001 + 0.0000i   0.0231 + 0.0236i   0.0231 - 0.0236i
   0.0318 + 0.0000i  -0.0269 + 0.0000i   0.0091 + 0.0104i   0.0091 - 0.0104i
   0.0316 + 0.0000i  -0.0045 + 0.0000i   0.0342 + 0.0007i   0.0342 - 0.0007i
   0.0311 + 0.0000i   0.0360 + 0.0000i   0.0524 - 0.0087i   0.0524 + 0.0087i
   0.0319 + 0.0000i   0.0312 + 0.0000i   0.0027 + 0.0155i   0.0027 - 0.0155i
   0.0318 + 0.0000i  -0.0289 + 0.0000i   0.0020 + 0.0219i   0.0020 - 0.0219i
   0.0315 + 0.0000i  -0.0443 + 0.0000i  -0.0338 - 0.0192i  -0.0338 + 0.0192i
   0.0332 + 0.0000i   0.0235 + 0.0000i   0.0167 - 0.0124i   0.0167 + 0.0124i
   0.0315 + 0.0000i   0.0027 + 0.0000i   0.0243 + 0.0013i   0.0243 - 0.0013i
   0.0319 + 0.0000i   0.0175 + 0.0000i  -0.0046 - 0.0309i  -0.0046 + 0.0309i
   0.0317 + 0.0000i   0.0557 + 0.0000i  -0.0098 - 0.0014i  -0.0098 + 0.0014i
   0.0313 + 0.0000i   0.0212 + 0.0000i  -0.0223 + 0.0191i  -0.0223 - 0.0191i
   0.0323 + 0.0000i   0.0356 + 0.0000i  -0.0118 - 0.0105i  -0.0118 + 0.0105i
   0.0314 + 0.0000i  -0.0577 + 0.0000i   0.0779 - 0.0041i   0.0779 + 0.0041i
   0.0307 + 0.0000i   0.0030 + 0.0000i  -0.0063 - 0.0134i  -0.0063 + 0.0134i
   0.0319 + 0.0000i  -0.0039 + 0.0000i  -0.0058 + 0.0129i  -0.0058 - 0.0129i
   0.0312 + 0.0000i   0.0347 + 0.0000i  -0.0366 - 0.0442i  -0.0366 + 0.0442i
   0.0325 + 0.0000i  -0.0011 + 0.0000i  -0.0280 + 0.0200i  -0.0280 - 0.0200i
   0.0312 + 0.0000i  -0.0077 + 0.0000i  -0.0296 - 0.0096i  -0.0296 + 0.0096i
   0.0324 + 0.0000i  -0.0425 + 0.0000i  -0.0147 + 0.0382i  -0.0147 - 0.0382i
   0.0312 + 0.0000i  -0.0644 + 0.0000i  -0.0261 + 0.0429i  -0.0261 - 0.0429i
   0.0312 + 0.0000i   0.0083 + 0.0000i  -0.0057 + 0.0083i  -0.0057 - 0.0083i
   0.0319 + 0.0000i   0.0254 + 0.0000i  -0.0134 + 0.0169i  -0.0134 - 0.0169i
   0.0314 + 0.0000i   0.0141 + 0.0000i   0.0157 + 0.0252i   0.0157 - 0.0252i
   0.0313 + 0.0000i  -0.0214 + 0.0000i   0.0289 - 0.0186i   0.0289 + 0.0186i
   0.0307 + 0.0000i  -0.0192 + 0.0000i   0.0094 - 0.0106i   0.0094 + 0.0106i
   0.0315 + 0.0000i  -0.0183 + 0.0000i  -0.0162 - 0.0007i  -0.0162 + 0.0007i
   0.0326 + 0.0000i  -0.0429 + 0.0000i  -0.0035 - 0.0382i  -0.0035 + 0.0382i
   0.0316 + 0.0000i  -0.0508 + 0.0000i   0.0035 + 0.0257i   0.0035 - 0.0257i
   0.0309 + 0.0000i   0.0179 + 0.0000i  -0.0078 - 0.0206i  -0.0078 + 0.0206i
   0.0319 + 0.0000i   0.0413 + 0.0000i  -0.0022 - 0.0098i  -0.0022 + 0.0098i
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   0.0317 + 0.0000i  -0.0031 + 0.0000i  -0.0167 + 0.0040i  -0.0167 - 0.0040i
   0.0309 + 0.0000i   0.0159 + 0.0000i  -0.0280 - 0.0189i  -0.0280 + 0.0189i
   0.0323 + 0.0000i  -0.0476 + 0.0000i   0.0083 - 0.0261i   0.0083 + 0.0261i
   0.0307 + 0.0000i   0.0298 + 0.0000i  -0.0325 - 0.0009i  -0.0325 + 0.0009i
   0.0316 + 0.0000i   0.0285 + 0.0000i  -0.0183 - 0.0247i  -0.0183 + 0.0247i
   0.0315 + 0.0000i  -0.0567 + 0.0000i  -0.0244 - 0.0071i  -0.0244 + 0.0071i
   0.0313 + 0.0000i   0.0201 + 0.0000i   0.0411 - 0.0002i   0.0411 + 0.0002i
   0.0320 + 0.0000i  -0.0018 + 0.0000i   0.0061 - 0.0094i   0.0061 + 0.0094i
   0.0309 + 0.0000i   0.0254 + 0.0000i   0.0439 + 0.0299i   0.0439 - 0.0299i
   0.0317 + 0.0000i   0.0288 + 0.0000i   0.0128 + 0.0338i   0.0128 - 0.0338i
   0.0318 + 0.0000i  -0.0168 + 0.0000i  -0.0075 - 0.0239i  -0.0075 + 0.0239i
   0.0325 + 0.0000i  -0.0385 + 0.0000i  -0.0064 + 0.0129i  -0.0064 - 0.0129i
   0.0306 + 0.0000i   0.0233 + 0.0000i   0.0001 - 0.0109i   0.0001 + 0.0109i
   0.0325 + 0.0000i   0.0418 + 0.0000i   0.0291 - 0.0095i   0.0291 + 0.0095i
   0.0316 + 0.0000i   0.0180 + 0.0000i   0.0056 + 0.0067i   0.0056 - 0.0067i
   0.0320 + 0.0000i   0.0119 + 0.0000i   0.0165 + 0.0189i   0.0165 - 0.0189i
   0.0310 + 0.0000i   0.0355 + 0.0000i  -0.0233 - 0.0203i  -0.0233 + 0.0203i
   0.0313 + 0.0000i   0.0287 + 0.0000i   0.0005 - 0.0149i   0.0005 + 0.0149i
   0.0321 + 0.0000i  -0.0950 + 0.0000i   0.0093 + 0.0075i   0.0093 - 0.0075i
   0.0319 + 0.0000i   0.0727 + 0.0000i   0.0022 + 0.0022i   0.0022 - 0.0022i
   0.0308 + 0.0000i   0.0096 + 0.0000i  -0.0068 + 0.0449i  -0.0068 - 0.0449i
   0.0315 + 0.0000i   0.0502 + 0.0000i  -0.0115 - 0.0104i  -0.0115 + 0.0104i
   0.0323 + 0.0000i   0.0344 + 0.0000i  -0.0030 - 0.0027i  -0.0030 + 0.0027i
   0.0323 + 0.0000i  -0.0062 + 0.0000i  -0.0311 + 0.0199i  -0.0311 - 0.0199i
   0.0325 + 0.0000i  -0.0366 + 0.0000i  -0.0112 + 0.0028i  -0.0112 - 0.0028i
   0.0311 + 0.0000i   0.0880 + 0.0000i  -0.0120 - 0.0230i  -0.0120 + 0.0230i
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   0.0306 + 0.0000i  -0.0225 + 0.0000i   0.0010 + 0.0315i   0.0010 - 0.0315i
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   0.0309 + 0.0000i   0.0020 + 0.0000i  -0.0127 + 0.0204i  -0.0127 - 0.0204i
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   0.0327 + 0.0000i   0.0244 + 0.0000i  -0.0074 + 0.0043i  -0.0074 - 0.0043i
   0.0308 + 0.0000i  -0.0068 + 0.0000i  -0.0116 - 0.0196i  -0.0116 + 0.0196i
   0.0309 + 0.0000i  -0.0193 + 0.0000i  -0.0011 - 0.0005i  -0.0011 + 0.0005i
   0.0310 + 0.0000i   0.0483 + 0.0000i  -0.0083 - 0.0421i  -0.0083 + 0.0421i
   0.0319 + 0.0000i  -0.0173 + 0.0000i  -0.0545 - 0.0059i  -0.0545 + 0.0059i
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   0.0312 + 0.0000i   0.0543 + 0.0000i   0.0134 - 0.0190i   0.0134 + 0.0190i
   0.0317 + 0.0000i   0.0103 + 0.0000i   0.0081 + 0.0325i   0.0081 - 0.0325i

  Columns 5 through 6

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  -0.0020 + 0.0079i  -0.0020 - 0.0079i
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  -0.0002 - 0.0511i  -0.0002 + 0.0511i
   0.0023 + 0.0107i   0.0023 - 0.0107i
   0.0083 + 0.0294i   0.0083 - 0.0294i
   0.0081 - 0.0200i   0.0081 + 0.0200i
  -0.0030 - 0.0041i  -0.0030 + 0.0041i
   0.0227 - 0.0125i   0.0227 + 0.0125i
  -0.0098 - 0.0105i  -0.0098 + 0.0105i
   0.0439 + 0.0126i   0.0439 - 0.0126i
  -0.0210 - 0.0286i  -0.0210 + 0.0286i
   0.0085 - 0.0271i   0.0085 + 0.0271i
   0.0175 + 0.0543i   0.0175 - 0.0543i
  -0.0327 + 0.0277i  -0.0327 - 0.0277i
   0.0006 + 0.0095i   0.0006 - 0.0095i
  -0.0135 - 0.0325i  -0.0135 + 0.0325i
  -0.0175 + 0.0447i  -0.0175 - 0.0447i
   0.0192 + 0.0096i   0.0192 - 0.0096i
   0.0039 - 0.0221i   0.0039 + 0.0221i
   0.0305 - 0.0007i   0.0305 + 0.0007i
  -0.0487 - 0.0324i  -0.0487 + 0.0324i
  -0.0262 + 0.0129i  -0.0262 - 0.0129i
  -0.0100 + 0.0330i  -0.0100 - 0.0330i
  -0.0405 + 0.0353i  -0.0405 - 0.0353i
  -0.0185 + 0.0356i  -0.0185 - 0.0356i
  -0.0131 - 0.0101i  -0.0131 + 0.0101i
   0.0104 - 0.0054i   0.0104 + 0.0054i
  -0.0000 - 0.0122i  -0.0000 + 0.0122i
   0.0067 - 0.0246i   0.0067 + 0.0246i
   0.0220 + 0.0155i   0.0220 - 0.0155i
  -0.0279 - 0.0117i  -0.0279 + 0.0117i
   0.0098 - 0.0034i   0.0098 + 0.0034i
  -0.0112 + 0.0515i  -0.0112 - 0.0515i
  -0.0288 - 0.0162i  -0.0288 + 0.0162i
  -0.0397 - 0.0070i  -0.0397 + 0.0070i
  -0.0314 - 0.0469i  -0.0314 + 0.0469i
   0.0094 - 0.0181i   0.0094 + 0.0181i
  -0.0290 + 0.0009i  -0.0290 - 0.0009i
  -0.0063 + 0.0083i  -0.0063 - 0.0083i
  -0.0337 - 0.0354i  -0.0337 + 0.0354i
  -0.0027 + 0.0091i  -0.0027 - 0.0091i
   0.0289 - 0.0106i   0.0289 + 0.0106i
  -0.0460 + 0.0048i  -0.0460 - 0.0048i
  -0.0034 + 0.0139i  -0.0034 - 0.0139i
   0.0016 - 0.0139i   0.0016 + 0.0139i
  -0.0027 + 0.0042i  -0.0027 - 0.0042i
  -0.0153 - 0.0099i  -0.0153 + 0.0099i
  -0.0248 + 0.0107i  -0.0248 - 0.0107i
  -0.0043 - 0.0036i  -0.0043 + 0.0036i
   0.0126 - 0.0076i   0.0126 + 0.0076i
  -0.0190 + 0.0338i  -0.0190 - 0.0338i
  -0.0425 - 0.0128i  -0.0425 + 0.0128i
   0.0219 + 0.0171i   0.0219 - 0.0171i
   0.0012 + 0.0050i   0.0012 - 0.0050i
   0.0037 - 0.0237i   0.0037 + 0.0237i
   0.0195 - 0.0400i   0.0195 + 0.0400i
   0.0056 + 0.0370i   0.0056 - 0.0370i
  -0.0003 - 0.0366i  -0.0003 + 0.0366i
   0.0426 + 0.0197i   0.0426 - 0.0197i
  -0.0139 - 0.0028i  -0.0139 + 0.0028i
   0.0352 + 0.0240i   0.0352 - 0.0240i
  -0.0472 - 0.0364i  -0.0472 + 0.0364i
  -0.0357 + 0.0350i  -0.0357 - 0.0350i
   0.0301 + 0.0626i   0.0301 - 0.0626i
   0.0367 - 0.0208i   0.0367 + 0.0208i
  -0.0255 - 0.0220i  -0.0255 + 0.0220i
  -0.0267 - 0.0158i  -0.0267 + 0.0158i
   0.0141 + 0.0288i   0.0141 - 0.0288i
   0.0334 - 0.0246i   0.0334 + 0.0246i
   0.0016 + 0.0116i   0.0016 - 0.0116i
  -0.0003 + 0.0106i  -0.0003 - 0.0106i
  -0.0156 - 0.0006i  -0.0156 + 0.0006i
  -0.0002 - 0.0070i  -0.0002 + 0.0070i
   0.0407 - 0.0040i   0.0407 + 0.0040i
   0.0032 + 0.0155i   0.0032 - 0.0155i
   0.0727 + 0.0304i   0.0727 - 0.0304i
  -0.0134 + 0.0229i  -0.0134 - 0.0229i
   0.0029 + 0.0226i   0.0029 - 0.0226i
   0.0176 - 0.0073i   0.0176 + 0.0073i
  -0.0029 - 0.0032i  -0.0029 + 0.0032i
  -0.0272 - 0.0385i  -0.0272 + 0.0385i
  -0.0059 + 0.0126i  -0.0059 - 0.0126i


EigVal7 =

   1.0e+02 *

  Columns 1 through 4

   5.0013 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0935 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0920 + 0.0148i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0920 - 0.0148i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i

  Columns 5 through 6

   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0483 + 0.0785i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0483 - 0.0785i

Elapsed time is 1.047719 seconds.

If you specify a number, k, after the matrix, the function will return the largest k eigenvalues.

tic
EigVal8=eigs(A,1)
toc

EigVal8 =

  500.1302

Elapsed time is 0.020651 seconds.

Published with MATLAB® R2016b