Computation of canonical matrices for chains and cycles of linear mappings

2003/10/09 by Vladimir V. Sergeichuk · 1 citation
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Matrix Theory and Algorithms #math.RT #msc:15A21 #msc:15A22 #msc:16G20

paper · pdf · doi:10.1016/j.laa.2003.07.001

published as Linear Algebra Appl. 376 (2004) 235-263 · 34 pages

openalex publication_date 2003/10/09 · arxiv created 2007/09/16 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

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

Cited by

• Matrices that are self-congruent only via matrices of determinant one