Singular Value Decomposition

SVD is an eigenvalue-like decomposition for rectangular matrices. If \(A\) is a \(m\) x \(n\) matrix then the SVD has the form
$$A=U\sum V^T$$
Where \(U\) is an \(m\)x\(n\) orthogonal matrix, \(V\) is a \(n\)x\(n\) orthogonal matrix, and \(\sum\) is a \(m\)x\(n\) diagonal matrix. The diagonal entries of \(\sum\) are singular values. The columns of \(U\) and \(V\) are orthonormal eigenvectors of \(AA^T\) and \(A^TA\) respectively. SVD is computed by a variant of the QR algorithm. It can also be computed with the Jacobi method which is useful on parallel computers.

[[N4SID]] – Performs CVD

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