Inverse eigenproblem for centrosymmetric and centroskew matrices and their approximation
Theoretical Computer Science - Algebraic and numerical algorithm
Journal of Computational and Applied Mathematics
Some properties of generalized K-centrosymmetric H-matrices
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Inverse eigenproblem for R-symmetric matrices and their approximation
Journal of Computational and Applied Mathematics
Parameterized inverse singular value problem for anti-bisymmetric matrices
Numerical Algorithms
Algorithms for {K,s+1}-potent matrix constructions
Journal of Computational and Applied Mathematics
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We show that the only real symmetric matrices whose spectrum is invariant modulo sign changes after either row or column reversal are the centrosymmetric matrices; moreover, we prove that the class of real symmetric centrosymmetric matrices can be completely characterized by this property. We also show that the only real symmetric matrices whose spectrum changes by multiplication by i after either row or column reversal are the skew-centrosymmetric matrices; here, too, we show that the class of real symmetric skew-centrosymmetric matrices can be completely characterized by this property of their eigenvalues. We prove both of these spectral characterizations as special cases of results for what we've called generalized centrosymmetric K-matrices and generalized skew-centrosymmetric K-matrices. Some results illustrating the application of the generalized centrosymmetric spectral characterization to other classes of real symmetric matrices are also given.