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Volume 15,     Number 1,     Spring 2007

 

INVOLUTIONS AND GENERALIZED
CENTROSYMMETRIC AND
SKEW-CENTROSYMMETRIC MATRICES
IYAD T. ABU-JEIB

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 + ρM are studied.

 

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