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arXiv · 2208.10149

Hoffman-Wielandt type inequality for block companion matrices of certain matrix polynomials

Pallavi . B·Shrinath Hadimani·Sachindranath Jayaraman
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Abstract

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 $D$.

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Pallavi . B, Shrinath Hadimani, Sachindranath Jayaraman. 2023-06-18. Hoffman-Wielandt type inequality for block companion matrices of certain matrix polynomials. https://arxiv.org/abs/2208.10149

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