Some properties of the block Toeplitz-Hessenberg matrices

In this paper, we have a t × t matrix polynomial that is defined by(…)of degree r that σ(L) = {λ ∈ C۱ : det L(λ) = ۰}.Here, we try to show a process for finding determinant of the block Toeplitz-Hessenbergmatrices from matrix polynomials by the block companion matrices.Also, we generalize a new version of Trudi’s formula for the block Toeplitz-Hessenbergmatrices. These tools are used to find eigenvalues, singularities, and stability andinstability of systems