Unified canonical forms for matrices over a differential ring

Roots and Canonical Forms for Circulant Matrices

Canonical Forms for Congruence of Matrices: a Tribute To

A canonical form for congruence of matrices was introduced by Turnbull and Aitken in 1932. More than 70 years later, in 2006, another canonical form for congruence has been introduced by Horn and Sergeichuk. The main purpose of this paper is to compare both canonical forms and provide a brief survey on the history of the canonical form for congruence.

Canonical matrices of bilinear and sesquilinear forms

Canonical matrices are given for • bilinear forms over an algebraically closed or real closed field; • sesquilinear forms over an algebraically closed field and over real quaternions with any nonidentity involution; and • sesquilinear forms over a field F of characteristic different from 2 with involution (possibly, the identity) up to classification of Hermitian forms over finite extensions of...

On canonical forms of ring-linear codes

This work presents an algorithm for the computation of canonical forms of linear codes over arbitrary finite chain rings under the action of the linear isometry group. It is a generalization of a previous work by the author on the canonization of linear codes over finite fields. The algorithm is based on the ideas of partition refinements and it will compute the automorphism group of the code a...

Canonical forms for doubly structured matrices and pencils

In this paper we derive canonical forms under structure preserving equivalence transformations for matrices and matrix pencils that have a multiple structure, which is either an H-selfadjoint or H-skew-adjoint structure, where the matrix H is a complex nonsingular Hermitian or skew-Hermitian matrix. Matrices and pencils of such multiple structures arise for example in quantum chemistry in Hartr...