A regularization algorithm for matrices of bilinear and sesquilinear forms

Abstract

We give an algorithm that uses only unitary transformations and for each square complex matrix constructs a *congruent matrix that is a direct sum of a nonsingular matrix and singular Jordan blocks.

18 pages

References in corpus (3)

• Classification problems for system of forms and linear mappings
• Congruences of a square matrix and its transpose
• Computation of the canonical form for the matrices of chains and cycles of linear mappings

Cited by in corpus (15)

• Canonical forms for complex matrix congruence and *congruence
• Canonical matrices of bilinear and sesquilinear forms
• Miniversal deformations of matrices of bilinear forms
• Change of the congruence canonical form of 2-by-2 and 3-by-3 matrices under perturbations and bundles of matrices under congruence
• Miniversal deformations of matrices under *congruence and reducing transformations
• Canonical Forms for Unitary Congruence and *Congruence
• Canonical matrices of isometric operators on indefinite inner product spaces
• Regularizing algorithm for mixed matrix pencils
• Tridiagonal canonical matrices of bilinear or sesquilinear forms and of pairs of symmetric, skew-symmetric, or Hermitian forms
• Matrices that are self-congruent only via matrices of determinant one
• Regularizing decompositions for matrix pencils and a topological classification of pairs of linear mappings
• Matrix Completion and Decomposition in Phase Bounded Cones
• Reduction of a pair of skew-symmetric matrices to its canonical form under congruence
• Classification of sesquilinear forms with the first argument on a subspace or a factor space
• Topological classification of sesquilinear forms: reduction to the nonsingular case