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

Authors:
Yongge Tian;Yoshio Takane
Affiliations:
China Economics and Management Academy, Central University of Finance and Economics, Beijing, China;Department of Psychology, McGill University, Montréal, Québec, Canada
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

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.