ON CAUCHY-TYPE BOUNDS FOR THE EIGENVALUES OF A SPECIAL CLASS OF MATRIX POLYNOMIALS

Abstract

Let Cm×m be the set of all m×m matrices whose entries are in C, the set of complex numbers. Then P(z):=∑j=0nAjzj, Aj∈Cm×m, 0≤j≤n is called a matrix polynomial. If An≠0, then P(z) is said to be a matrix polynomial of degree n. In this paper we prove some results for the bound estimates of the eigenvalues of some lacunary type of matrix polynomials.