On the inversion of a particular matrix
R. Hoard, F. L. Huband · IEEE Transactions on Automatic Control · 1972
Necessary and sufficient conditions for the nonsingularity of a particularmn \times mnpartitioned matrixCare given in terms of lower orderm \times mmatrices. The matrixCis formed by adding a block diagonal matrix to a partitioned matrix, each of whose submatrices are identical. Analytical formulas are given for both the determinant and the inverse ofC.