论文标题
矩阵公式的解决方案$ p（x）= a $，带有多项式函数$ p（λ）$ a $ \ m m i \ mathbb {q} $
Solutions of the matrix equation $p(X)=A$, with polynomial function $p(λ)$ over field extensions of $\mathbb{Q}$
论文作者
论文摘要
令$ \ mathbb {h} $为$ \ mathbb {q} \ subset \ mathbb {h} \ subset \ subset \ mathbb {c} $的字段，让$ p（λ）$为$ \ mathbb {h} [λ] $，然后让$ a \ a \ a \ a \ n \ n \ n \ n \ n \ n \ n \ n \ ar n} $是非d的。在本文中，我们考虑找到解决方案$ x \ in \ mathbb {h}^{n \ times n} $ to $ p（x）= a $的问题。从M.P. Drazin。在额外的条件下，我们提供了这种解决方案的明确结构。还将讨论与贬义案例的相似性和差异。 本文中所需的工具之一是一种新的规范形式，可能具有独立的兴趣。它将理性规范形式的要素与约旦规范形式的要素结合在一起。
Let $\mathbb{H}$ be a field with $\mathbb{Q}\subset\mathbb{H}\subset\mathbb{C}$, and let $p(λ)$ be a polynomial in $\mathbb{H}[λ]$, and let $A\in\mathbb{H}^{n\times n}$ be nonderogatory. In this paper we consider the problem of finding a solution $X\in\mathbb{H}^{n\times n}$ to $p(X)=A$. A necessary condition for this to be possible is already known from a paper by M.P. Drazin. Under an additional condition we provide an explicit construction of such solutions. The similarities and differences with the derogatory case will be discussed as well. One of the tools needed in the paper is a new canonical form, which may be of independent interest. It combines elements of the rational canonical form with elements of the Jordan canonical form.
