Matrix analysis
Topics in matrix analysis
Singular value decompositions of complex symmetric matrices
Journal of Computational and Applied Mathematics
Matrix computations (3rd ed.)
Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
SIAM Journal on Matrix Analysis and Applications
| Hi-index | 7.29 |
The classical singular value decomposition for a matrix A@?C^m^x^n is a canonical form for A that also displays the eigenvalues of the Hermitian matrices AA^* and A^*A. In this paper, we develop a corresponding decomposition for A that provides the Jordan canonical forms for the complex symmetric matrices AA^T and A^TA. More generally, we consider the matrix triple (A,G,G@?), where G@?C^m^x^m,G@?@?C^n^x^n are invertible and either complex symmetric or complex skew-symmetric, and we provide a canonical form under transformations of the form (A,G,G@?)@?(X^TAY,X^TGX,Y^TG@?Y), where X,Y are nonsingular.