✦ LIBER ✦
The solvability conditions for inverse eigenproblem of symmetric and anti-persymmetric matrices and its approximation
✍ Scribed by Dongxiu Xie; Xiyan Hu; Lei Zhang
- Publisher
- John Wiley and Sons
- Year
- 2003
- Tongue
- English
- Weight
- 104 KB
- Volume
- 10
- Category
- Article
- ISSN
- 1070-5325
- DOI
- 10.1002/nla.285
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✦ Synopsis
Abstract
The problem of generating a matrix A with specified eigen‐pair, where A is a symmetric and anti‐persymmetric matrix, is presented. An existence theorem is given and proved. A general expression of such a matrix is provided. We denote the set of such matrices by 𝒮𝒜𝒮~E~^n^. The optimal approximation problem associated with 𝒮𝒜𝒮~E~^n^ is discussed, that is: to find the nearest matrix to a given matrix A* by A∈𝒮𝒜𝒮~E~^n^. The existence and uniqueness of the optimal approximation problem is proved and the expression is provided for this nearest matrix. Copyright © 2002 John Wiley & Sons, Ltd.