# Difference between revisions of "proof of Theorem 1"

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The above proof is the proof of Theorem 2.1 in <ref name="WTH2009">Daniela M. Witten, Robert Tibshirani, and Trevor Hastie. (2009) "A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis". ''Biostatistics'', 10(3):515–534.</ref> | The above proof is the proof of Theorem 2.1 in <ref name="WTH2009">Daniela M. Witten, Robert Tibshirani, and Trevor Hastie. (2009) "A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis". ''Biostatistics'', 10(3):515–534.</ref> | ||

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## Latest revision as of 08:45, 30 August 2017

Let [math]\textbf{u}_k[/math] and [math]\textbf{v}_k[/math] denote column k of [math]\textbf{U}[/math] and [math]\textbf{V}[/math] respectively, We prove the theorem by expanding out the squared Frobenius norm and rearranging terms:

The above proof is the proof of Theorem 2.1 in <ref name="WTH2009">Daniela M. Witten, Robert Tibshirani, and Trevor Hastie. (2009) "A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis". *Biostatistics*, 10(3):515–534.</ref>

## References

<references />