Structure ranks of matrices

AbstractThe structure rank of a matrix, i.e. the maximum order of a nonsingular submatrix all of whose entries are located in a given structure (a subset of M × N, where M, N are the row- and column-index sets, respectively) were previously studied for the off-diagonal part. Here, results on more general ranks, e.g. off-block-diagonal, strictly upper-triangular, and strictly upper-block-triangular, are presented. In particular, it is shown that for a nonsingular matrix A, in each of the last-mentioned three cases, the ranks of A and A-1 coincide