Singular-Value Decomposition via Gradient and Self-Equivalent Flows

The task of finding the singular-value decomposition (SVD) of a finite-dimensional complex Iinear operator is here addressed via gradient flows evolving on groups of complex unitary matrices and associated self-equivalent flows. The work constitutes a generalization of that of Brockett on the diagonalization of real symmetric matrices via gradient flows on orthogonal matrices and associated isospectral flows, It complements results of Symes, Chu, and other authors on continuous analogs of the classical QR algorithm as well as earlier work by the authors on SVD via gradient flows on positive definite matrices.