Abstract
The theory underlying certain representations of a matrix as sum of products of matrices in algebras is here revisited with the aim of reducing it at its very heart. In this way we obtain a simple and general theorem that extends some known results.
References
C. Di Fiore and P. Zellini,Matrix decompositions using displacement rank and classes of commutative matrix algebras, Linear Algebra Appl.229 (1995), 49–99.
I. Gohberg and V. Olshevsky,Circulants, displacements and decompositions of matrices, Integral Equations and Operator Theory15 (1992), 730–743.
K. Rost,Generalized companion matrices and matrix representations for generalized Bezoutians, Linear Algebra Appl.193 (1993), 151–172.