Computation of the canonical form for the matrices of chains and cycles of linear mappings

Abstract

Paul Van Dooren [Linear Algebra Appl. 27 (1979) 103-140] constructed an algorithm for the computation of all irregular summands in Kronecker's canonical form of a matrix pencil. The algorithm is numerically stable since it uses only unitary transformations. We extend Paul Van Dooren's algorithm to the matrices of a cycle of linear mappings.

arXiv comment34 pages

References in corpus (3)

• Canonical matrices for linear matrix problems
• Complexity of matrix problems
• Applications of the duality method to generalizations of the Jordan canonical form

Cited by in corpus (11)

• A regularization algorithm for matrices of bilinear and sesquilinear forms
• Regularizing algorithm for mixed matrix pencils
• Topological classification of chains of linear mappings
• Matrices that are self-congruent only via matrices of determinant one
• Solvability and uniqueness criteria for generalized Sylvester-type equations
• Cycles of linear and semilinear mappings
• Classification of linear mappings between indefinite inner product spaces
• Regularizing decompositions for matrix pencils and a topological classification of pairs of linear mappings
• Classification of sesquilinear forms with the first argument on a subspace or a factor space
• Reduction of a pair of skew-symmetric matrices to its canonical form under congruence
• Miniversal deformations of chains of linear mappings