We review some definitions and basic facts related to polynomial matrices. Usually, unless stated otherwise, we deal with real polynomial matrices, whose coefficient matrices are real. If is the unit matrix then P is said to be monic . Tall and wide A polynomial or other matrix is tall if it has at least as many rows as columns. It is wide if it has at least as many columns as rows.
Similar definitions hold for full row rank and full rank .
The normal rank of a polynomial matrix P equals Similar definitions apply to the notions of normal column rank and normal row rank. A square polynomial matrix is nonsingular if it has full normal rank. Top Let the elements of the k m polynomial matrix P be Then the numbers are the row and the column degrees of P, respectively. Top Suppose that P has column and row degrees respectively. It is row reduced if its row leading coefficient matrix has full row rank.