The number of invariant polynomials of a matrix with prescribed off-diagonal blocks Original Research Article

Let A be an n × n matrix over an arbitrary field F of the form image where A1, 1 set membership, variant Fp × p, and A2, 2 set membership, variant Fq × q, and p + Q = n. We characterize the possible number of nontrivial invariant polynomials of A, when the submatrices A1, 2 and A2, 1 are prescribed.