Authors
Iyad T. Abu-Jeib
Pages From
1
Pages To
10
Journal Name
Can. Appl. Math. Q.
Volume
15
Issue
1
Keywords
involutory matrix, generalized skew-centrosymmetric, generalized centrosymmetric, $K$-symmetric, $K$-skew-symmetric, skew-symmetric, rank-one
Abstract
We present new results and simple short proofs for known theorems about generalized
centrosymmetric matrices and generalized skew-centrosymmetric (centroskew) matrices. We also
make a comparison between the identity matrix and a nontrivial involutory matrix $K$
by
studying the eigensystem of $K+M$, where $M$ is a structured matrix, with the goal of expressing
this system entirely in terms of the corresponding eigensystem of $M$. Also, properties of
some parametric families of the form $K+\rho M$ are studied.