General PT-Symmetric Matrices

General PT-Symmetric Matrices

Three ways of constructing a non-Hermitian matrix with possible all real eigenvalues are discussed. They are PT symmetry, pseudo-Hermiticity, and generalized PT symmetry. Parameter counting is provided for each class. All three classes of matrices have more real parameters than a Hermitian matrix wi...

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Veröffentlicht in:arXiv.org 2012-12
Hauptverfasser: Jia-wen, Deng, Guenther, Uwe, Qing-hai Wang
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Eigenvalues
Mathematical analysis
Matrix methods
Operators (mathematics)
Parameters
Symmetry
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description Three ways of constructing a non-Hermitian matrix with possible all real eigenvalues are discussed. They are PT symmetry, pseudo-Hermiticity, and generalized PT symmetry. Parameter counting is provided for each class. All three classes of matrices have more real parameters than a Hermitian matrix with the same dimension. The generalized PT-symmetric matrices are most general among the three. All self-adjoint matrices process a generalized PT symmetry. For a given matrix, it can be both PT-symmetric and P'-pseudo-Hermitian with respect to some P' operators. The relation between corresponding P and P' operators is established. The Jordan block structures of each class are discussed. Explicit examples in 2x2 are shown.
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subjects Eigenvalues
Mathematical analysis
Matrix methods
Operators (mathematics)
Parameters
Symmetry
title General PT-Symmetric Matrices
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