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arXiv · 1212.1861

General PT-Symmetric Matrices

Jia-wen Deng·Uwe Guenther·Qing-hai Wang
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Abstract

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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Jia-wen Deng, Uwe Guenther, Qing-hai Wang. 2012-12-09. General PT-Symmetric Matrices. https://arxiv.org/abs/1212.1861

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