Matrices with multiple symmetry properties: applications of centro-Hermitian and per-Hermitian matrices. (English) Zbl 0957.15019

In this paper the authors introduce three matrix patterns, essentially asking that the matrix is either real or pure imaginary or zero, that combined with the twelve known symmetric patterns (symmetric, centrosymmetric, persymmetric, Hermitian, centro-Hermitian, per-Hermitian, skew-symmetric, skew-centrosymmetric, skew-persymmetric, skew-Hermitian, skew-centro-Hermitian, skew-per-Hermitian) form a Steiner triple system.
In addition, using a group of operators on the linear group over the complex numbers they reach types of matrices that satisfy sets of patterns, and that yield to unique decompositions into matrices of the same type. Also, they extend the symmetric patterns to vectors, and symmetric properties on matrices are deduced from the existence of basis of eigenvectors satisfying certain symmetric properties.


15B57 Hermitian, skew-Hermitian, and related matrices
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15A45 Miscellaneous inequalities involving matrices
65F25 Orthogonalization in numerical linear algebra
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