Singular values, diagonal elements, and extreme matrices
β Scribed by Hector F. Miranda
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 75 KB
- Volume
- 305
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
β¦ Synopsis
For complex matrices A and B there are inequalities related to the diagonal elements of AB and the singular values of A and B. We study the conditions on the matrices for which those inequalities become equalities. In all cases, the conditions are both necessary and sufficient.
π SIMILAR VOLUMES
We consider the problem of constructing nonnegative matrices with prescribed extremal singular values. In particular, given 2n -1 real numbers Ο ( j) 1 and Ο ( j) j , j = 1, . . . , n, we construct an n Γ n nonnegative bidiagonal matrix B and an n Γ n nonnegative semi-bordered diagonal matrix C, suc
Thomspon and Sing's result on the singular values and the diagonal elements of a complex n X n matrix has been recently extended to arbitrary m matrices, by Lei and by Miranda and Thompson independently. The real case in which the determinant of the product of the m real matrices is nonnegative (or