论文标题
Hoffman-Wielandt类型的不平等，用于某些矩阵多项式的块伴侣矩阵
Hoffman-Wielandt type inequality for block companion matrices of certain matrix polynomials
论文作者
论文摘要
具有单一/双随机系数的矩阵多项式构成了该手稿的主题。我们证明，如果$ p（λ）$是二次矩阵多项式，其系数是单位矩阵或双随机矩阵，则在这些系数的某些条件下，相应的块伴随矩阵$ c $是可调的。因此，如果$ q（λ）$是另一个二次矩阵多项式，带有相应的块伴侣矩阵$ d $，则霍夫曼 - 韦兰特类型的不平等适用于块伴侣矩阵$ c $和$ d $。
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 $D$.
