Some results on numerical ranges and factorizations of matrix polynomials
Alexander S. Markus, Leiba Rodman · Linear and Multilinear Algebra · 1997
Some new factorization theorems for monic matrix polynomials are obtained. These theorems are based on the numerical range having the number of connected components equal to the degree of the polynomial. For second degree polynomials, sufficient conditions are given for the numerical range to have two connected components.