论文标题
矩阵Kronecker乘积的最小多项式的明确表达。矩阵对数和矩阵指数的显式公式
An explicit expression for the minimal polynomial of the Kronecker product of matrices. Explicit formulas for matrix logarithm and matrix exponential
论文作者
论文摘要
使用$ \ MATHCAL {P} $ - 矩阵的规范形式，我们根据这些矩阵的最小多项式来得出给定矩阵家族的Kronecker乘积的最小多项式。这使我们允许我们证明产品$ \ prod \ limits_ {i = 1}^{m} l（p_ {i}）$，$ l（p_ {i}）$是一组线性复发序列，一组字段$ f $，具有特征性的pog p_ p_ p_ p_ p_ i} $ p $ l（p $ l（p）$ l（p） $ p_ {i} $，$ 1 \ leq i \ leq m $的伴侣矩阵的产品。另外，我们展示了如何从$ \ Mathcal {p} $ - 任意复杂矩阵$ a $的规范形式，$ \ MATHCAL {p} $ - 矩阵函数的规范形式$ e e^{ta} $和$ a $ a $ a $的次数。
Using $\mathcal{P}$-canonical forms of matrices, we derive the minimal polynomial of the Kronecker product of a given family of matrices in terms of the minimal polynomials of these matrices. This, allows us to prove that the product $\prod\limits_{i=1}^{m}L(P_{i})$, $L(P_{i})$ is the set of linear recurrence sequences over a field $F$ with characteristic polynomial $P_{i}$, is equal to $L(P)$ where $P$ is the minimal polynomial of the Kronecker product of the companion matrices of $P_{i}$, $1\leq i\leq m$. Also, we show how we deduce from the $\mathcal{P}$-canonical form of an arbitrary complex matrix $A$, the $\mathcal{P}$-canonical form of the matrix function $e^{tA}$ and a logarithm of $A$.
