Content deleted Content added
→Other examples: replaced dead link with a link that works |
Alexwagner (talk | contribs) m The punctuation of the original statement was confusing. After reading it several times, this is what I think was meant by it. |
||
Line 22:
where <math>r \leq \min\{m,n\}</math> is the rank of {{tmath|\mathbf M.}}
The SVD is not unique
The term sometimes refers to the '''compact SVD''', a similar decomposition {{tmath|\mathbf M {{=}} \mathbf{U\Sigma V}^*}} in which {{tmath|\mathbf \Sigma}} is square diagonal of size {{tmath|r \times r,}} where {{tmath|r \leq \min\{m,n\} }} is the rank of {{tmath|\mathbf M,}} and has only the non-zero singular values. In this variant, {{tmath|\mathbf U}} is an {{tmath|m \times r}} [[semi-orthogonal matrix|semi-unitary matrix]] and <math>\mathbf{V}</math> is an {{tmath|n \times r}} [[semi-orthogonal matrix|semi-unitary matrix]], such that <math>\mathbf U^* \mathbf U = \mathbf V^* \mathbf V = \mathbf I_r.</math>
| |||