Frontiers of Mathematics in China >
Hermitizable, isospectral complex matrices or differential operators
Received date: 07 May 2018
Accepted date: 24 Jul 2018
Published date: 02 Jan 2019
Copyright
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.
Key words： Real spectrum; symmetrizable; Hermitizable; isospectral; matrix; differential operator
Mu-Fa CHEN . Hermitizable, isospectral complex matrices or differential operators[J]. Frontiers of Mathematics in China, 2018 , 13(6) : 1267 -1311 . DOI: 10.1007/s11464-018-0716-x
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