Inverses of \(2\times 2\) block matrices
Explicit inverse formulas for \(2\times 2\) block matrices with three different partitions are derived. A complete treatment is given. The results are used to get inverses of \(2\times 2\) block triangular matrices. The main theorems are also applied to structured matrices including bisymmetric, Hamiltonian, Hankel, Toeplitz, circulant, Hermitian, centro-Hermitian, and their skew Hermitian matrices. The completion problem of a \(2\times 2\) block matrix and its inverse is discussed.
scientific article; zbMATH DE number 1781464
scientific article