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. © 2009 Elsevier Ltd. All rights reserved.
Tian, Y., & Takane, Y. (2009). The inverse of any two-by-two nonsingular partitioned matrix and three matrix inverse completion problems. Computers and Mathematics with Applications, 57(8), 1294–1304. https://doi.org/10.1016/j.camwa.2009.01.025