The rank of powers of matrices in a block triangular form
A graph theoretic upper bound for the rank of sufficiently high powers of a complex valued matrix are given. Namely, assuming a lower block triangular form of the matrix, the bound is given in terms of the rank of the powers of its diagonal blocks. An index theorem, which relates the index of the matrix to the indices of its diagonal blocks, is obtained as a corollary.
scientific article; zbMATH DE number 4069077