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

作者：

Highlights：

• The quadratic matrix equation X*AX+B*X+D=0 is discussed.

• The necessary and sufficient conditions for the existence and the explicit expression for the general solution are obtained.

• The method is based on the singular value decomposition and spectral decomposition.

• A type of inverse statistical problem which arises in satellite meteorology is discussed.

摘要

•The quadratic matrix equation X*AX+B*X+D=0 is discussed.•The necessary and sufficient conditions for the existence and the explicit expression for the general solution are obtained.•The method is based on the singular value decomposition and spectral decomposition.•A type of inverse statistical problem which arises in satellite meteorology is discussed.

论文关键词：Quadratic matrix equation,Moore–Penrose inverse,Singular value decomposition,Spectral decomposition

论文评审过程：Received 29 August 2020, Revised 7 May 2021, Accepted 16 June 2021, Available online 27 June 2021, Version of Record 27 June 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126463