Hoffman-Wielandt type inequality for block companion matrices of certain matrix polynomials
B Pallavi, Shrinath Hadimani, Sachindranath Jayaraman · arXiv (Cornell University) · 2022
Matrix polynomials with unitary/doubly stochastic coefficients form the subject matter of this manuscript. We prove that if $P(λ)$ is a quadratic matrix polynomial whose coefficients are either unitary matrices or doubly stochastic matrices, then under certain conditions on these coefficients, the corresponding block companion matrix $C$ is diagonalizable. Consequently, if $Q(λ)$ is another quadratic matrix polynomial with corresponding block companion matrix $D$, then a Hoffman-Wielandt type inequality holds for the block companion matrices $C$ and $D$.