Ranks of Hermitian and skew-Hermitian solutions to the matrix equation
โ Scribed by Yonghui Liu; Yongge Tian; Yoshio Takane
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 192 KB
- Volume
- 431
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
A simple representation of the general rank-constrained Hermitian nonnegative-definite (positive-definite) solution to the matrix equation AXA \* = B is derived. As medium steps, the general Hermitian solution and the general Hermitian nonnegative-definite (positive-definite) solution to the matrix
A conjecture that the nonlinear matrix equation always has a unique Hermitian positive definite solution is proved. Some bounds of the unique Hermitian positive definite solution are given.
In this paper, the Hermitian positive definite solutions of the matrix equation X s + A \* X -t A = Q are considered, where Q is an Hermitian positive definite matrix, s and t are positive integers. Necessary and sufficient conditions for the existence of an Hermitian positive definite solution are