The inverse of any two-by-two nonsingular partitioned matrix and three matrix inverse completion problems

被引：15

作者：

Tian, Yongge ^{[1
]}

Takane, Yoshio ^{[2
]}

机构：

[1] Cent Univ Finance & Econ, China Econ & Management Acad, Beijing, Peoples R China

[2] McGill Univ, Dept Psychol, Montreal, PQ, Canada

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2009年 / 57卷 / 08期

关键词：

Inverse of matrix; Moore-Penrose inverse of matrix; Matrix completion problem; Hermitian matrix; Skew-Hermitian matrix; Rank formulas for partitioned matrices; INVERTIBLE COMPLETIONS; RANK;

D O I：

10.1016/j.camwa.2009.01.025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A formula for the inverse of any nonsingular matrix partitioned into two-by-two blocks is derived through a decomposition of the matrix itself and generalized inverses of the submatrices in the matrix. The formula is then applied to three matrix inverse completion problems to obtain their complete solutions. (c) 2009 Elsevier Ltd. All rights reserved.

引用

页码：1294 / 1304

页数：11

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