Mr. Integral
Math notes/Linear Algebra/SVD and Engineering Computation

Singular Value Decomposition — Cheat sheet

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Core rule

A=UΣVT,Avi=σiui,σi2 are eigenvalues of ATA.A=U\Sigma V^T,\quad Av_i=\sigma_i u_i,\quad \sigma_i^2\text{ are eigenvalues of }A^TA.

Watch for

Singular values are nonnegative and exist for rectangular matrices. Do not divide by a zero singular value.