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The general common nonnegative-definite and positive-definite solutions to the matrix equations AXA∗ = BB∗ and CXC∗ = DD∗

✍ Scribed by Xian Zhang; Mei-Yu Cheng

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
276 KB
Volume
17
Category
Article
ISSN
0893-9659

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✦ Synopsis

We give necessaxy and sufficient conditions for the existence of a common nonnegativedefinite (positive-definite) solution to the pair of matrix equations AXA* = BB* and CXC* = DD*, and derive a representation of the general common nonnegative-definite (positive-definite) solution to these two equations when they have such common solutions. This paper can be viewed as a supplementary version of that derived by Young et al. [1] since GroI3 [2] has given a counterexample to point out a mistake in their basic Theorem 1. The presented example shows the advantage of the proposed approach. (~) 2004 Elsevier Ltd. All rights reserved.

📜 SIMILAR VOLUMES

The rank-constrained Hermitian nonnegati
The rank-constrained Hermitian nonnegative-definite and positive-definite solutions to the matrix equation AXA∗=B
✍ Xian Zhang; Mei-yu Cheng 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 118 KB

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