Hermitizable,isospectral complex matrices or differential operators |
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Authors: | Mu-Fa Chen |
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Institution: | School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems (Beijing Normal University), Ministry of Education, Beijing 100875, China |
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Abstract: | The main purpose of the paper is looking for a larger class of matrices which have real spectrum. The first well-known class having this property is the symmetric one, then is the Hermite one. This paper introduces a new class, called Hermitizable matrices. The closely related isospectral problem, not only for matrices but also for differential operators is also studied. The paper provides a way to describe the discrete spectrum, at least for tridiagonal matrices or one-dimensional differential operators. Especially, an unexpected result in the paper says that each Hermitizable matrix is isospectral to a birth–death type matrix (having positive sub-diagonal elements, in the irreducible case for instance). Besides, new efficient algorithms are proposed for computing the maximal eigenpairs of these class of matrices. |
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Keywords: | Real spectrum symmetrizable Hermitizable isospectral matrix differential operator |
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