Singular Value Decomposition is a factorization of a real or complex matrix. It generalizes the eigendecomposition of a square matrix to any \(m \times n\) matrix.

Formula:

\(A = U \Sigma V^T\)

• \(A\) is an \(m \times n\) matrix.
• \(U\) is an \(m \times m\) orthogonal matrix.
• \(\Sigma\) is an \(m \times n\) diagonal matrix with non-negative real numbers on the diagonal, known as the singular values.
• \(V^T\) is the transpose of an \(n \times n\) orthogonal matrix \(V\).

The columns of \(V\) are the eigenvectors of \(A^T A\), and the columns of \(U\) are the eigenvectors of \(A A^T\).