The solutions to the quadratic matrix equation X*AX+B*X+D=0

Yongxin Yuan, Lina Liu, Huiting Zhang and Hao Liu

Applied Mathematics and Computation, 2021, vol. 410, issue C

Abstract: The necessary and sufficient conditions for the existence and the explicit expression for the general solution are obtained for the quadratic matrix equation X*AX+B*X+D=0, where A∈Cn×n,B∈Cn×p and D∈Cp×p are given complex matrices with D*=D and A*=A, and (·)* denotes the conjugate transpose of a complex matrix. Furthermore, a type of inverse statistical problem which arises in satellite meteorology is discussed.

Keywords: Quadratic matrix equation; Moore–Penrose inverse; Singular value decomposition; Spectral decomposition (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:410:y:2021:i:c:s009630032100552x

DOI: 10.1016/j.amc.2021.126463

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