Journal article
Real factorization of positive semidefinite matrix polynomials
Linear algebra and its applications, v 683, pp 125-150
15 Feb 2024
Abstract
Suppose Q(x) is a real n x n regular symmetric positive semidefinite matrix polynomial. Then it can be factored as Q(x) = G(x)TG(x), where G(x) is a real n x n matrix polynomial with degree half that of Q(x) if and only if det(Q(x)) is the square of a nonzero real polynomial. We provide a constructive proof of this fact, rooted in finding a skew-symmetric solution to a modified algebraic Riccati equation XSX- XR +RTX + P = 0, where P, R, S are real n x n matrices with P and S real symmetric. In addition, we provide a detailed algorithm for computing the factorization. (c) 2023 Elsevier Inc. All rights reserved.
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Details
- Title
- Real factorization of positive semidefinite matrix polynomials
- Creators
- Sarah Gift - Drexel Univ, Dept Math, Philadelphia, PA 19104 USAHugo J. Woerdeman - Drexel University, Mathematics
- Publication Details
- Linear algebra and its applications, v 683, pp 125-150
- Publisher
- Elsevier
- Number of pages
- 26
- Grant note
- DMS 2000037 / National Science Foundation; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001140285800001
- Scopus ID
- 2-s2.0-85179886956
- Other Identifier
- 991021861306804721
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- Web of Science research areas
- Mathematics
- Mathematics, Applied