论文标题
一般表示的理性矩阵的线性化
Linearizations of rational matrices from general representations
论文作者
论文摘要
我们构建了一个以通用形式$ r（λ）= d（λ）+c（λ）a（λ）a（λ）^{ - 1} b（λ）$写成的理性矩阵$ r（λ）$的新系列。这种表示始终存在，并不是唯一的。新的线性化是由多项式矩阵$ d（λ）$和$ a（λ）$的线性化构建的，其中每个线性都可以用任何多项式为基础表示。此外，我们还展示了如何恢复特征向量时，当$ r（λ）$是常规的，而最小的基础和最小索引，当$ r（λ）$是单数时，从这个家庭中的线性化。
We construct a new family of linearizations of rational matrices $R(λ)$ written in the general form $R(λ)= D(λ)+C(λ)A(λ)^{-1}B(λ)$, where $D(λ)$, $C(λ)$, $B(λ)$ and $A(λ)$ are polynomial matrices. Such representation always exists and are not unique. The new linearizations are constructed from linearizations of the polynomial matrices $D(λ)$ and $A(λ)$, where each of them can be represented in terms of any polynomial basis. In addition, we show how to recover eigenvectors, when $R(λ)$ is regular, and minimal bases and minimal indices, when $R(λ)$ is singular, from those of their linearizations in this family.
