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On the counteridentity matrix

Authors: 
Iyad T. Abu-Jeib
Journal Name: 
Missouri J. Math. Sci.
Volume: 
17
Issue: 
1
Pages From: 
26
To: 
34
Date: 
Saturday, January 1, 2005
Keywords: 
Counteridentity, exchange matrix, flip matrix, anti-identity, eigenvalue, eigenvector, persymmetric, centrosymmetric, skew-centrosymmetric, skew-symmetric, rank-one, diagonal matrix.
Abstract: 
We make a comparison between the identity matrix and the counteridentity matrix by studying the eigensystem of $J+M$, where $J$ is the counteridentity matrix and $M$ 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 $J+\rho M$ are studied.
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