Singular Value Decomposition (SVD)

Decomposition of a matrix \(A\) as

\begin{equation*} A = U \Sigma V^T \end{equation*}

Where, \(U\) and \(V\) are orthogonal matrices and \(\Sigma\) is a diagonal matrix.

This implies:

\begin{equation*} A V = \Sigma U \end{equation*} \begin{equation*} U^T A = \Sigma V^T \end{equation*}

See:

• Spectral Algorithms
• Singular Vector

Alogrithms for SVD:

• https://academic.oup.com/nsr/article/10/6/nwad083/7086135?login=false
• https://research.facebook.com/blog/2014/9/fast-randomized-svd/
• https://arxiv.org/abs/2402.09754
• https://www.youtube.com/watch?v=Gc1NBpGroyE
• https://www.youtube.com/watch?v=vDSi271vUWk