Constructing a real symmetric toeplitz matrix with two prescribed eigenpairs
Constructing a real symmetric toeplitz matrix with two prescribed eigenpairs
- Author(s): Bei Chen ; Dandan Xu ; Xiusong Gu
- DOI: 10.1049/cp.2012.1072
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- Author(s): Bei Chen ; Dandan Xu ; Xiusong Gu Source: International Conference on Automatic Control and Artificial Intelligence (ACAI 2012), 2012 p. 693 – 696
- Conference: International Conference on Automatic Control and Artificial Intelligence (ACAI 2012)
- DOI: 10.1049/cp.2012.1072
- ISBN: 978-1-84919-537-9
- Location: Xiamen, China
- Conference date: 3-5 March 2012
- Format: PDF
This paper is concerned with the inverse eigenvalue problems for symmetric Toeplitz matrices. A kind of inverse problem for constructing a real symmetric Toeplitz matrix from the given k eigenpairs is proposed. By using the special structure of symmetric Toeplitz matrices, the Kronecker product and the vec operator of matrices, the problem is transformed into the system of linear equations. Some necessary and sufficient conditions for the solvability of the problem are given. The general solutions of the problem are presented.
Inspec keywords: Toeplitz matrices; eigenvalues and eigenfunctions; inverse problems; mathematical operators
Subjects: Algebra; Algebra; Algebra; Algebra, set theory, and graph theory
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