Inverse eigenvalue problems for bisymmetric matrices under a central principal submatrix constraint. (English) Zbl 1211.15013
A matrix \(A\in {\mathbb R}^{n\times n}\) is called a bisymmetric matrix if it is symmetric and symmetric about the anti-diagonal. An inverse eigenvalue problem for bisymmetric matrices under a central principal submatrix constraint (Problem 1 in the paper) is studied as well as the corresponding optimal approximation problem (Problem 2 in the paper). Some necessary and sufficient conditions are given for the solvability of the inverse eigenvalue problem. An expression for its general solution is obtained. A solution to the corresponding optimal approximation problem is provided.
Reviewer: Tin Yau Tam (Auburn)
MSC:
| 15A18 | Eigenvalues, singular values, and eigenvectors |
| 15A29 | Inverse problems in linear algebra |
| 15B57 | Hermitian, skew-Hermitian, and related matrices |
| 65F18 | Numerical solutions to inverse eigenvalue problems |
Keywords:
bisymmetric matrix; central principal submatrix; inverse eigenvalue problem; optimal approximation problemReferences:
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