论文标题
在矩阵的半不变
On Semi-Invariants of a Matrix
论文作者
论文摘要
对于一个代数封闭的特征性零和非singular矩阵$ a \ in \ mbox {gl} _n（k）$，$ a $ a $的半不变的多项式定义为多项式$ p（x）= $ p（xa）=λp（x）$ for K $中的某些$λ\。在本文中，我们将$ a $的所有半不变的多项式分类为规范构造的基础，这些基础将在文本中精确。
For an algebraically closed field $K$ of characteristic zero and a non-singular matrix $A\in \mbox{GL}_n(K)$, a semi-invariant polynomial of $A$ is defined to be a polynomial $p(x)=p(x_1,\dots,x_n)$ with coefficients in $K$ such that $p(xA)=λp(x)$ for some $λ\in K$. In this article, we classify all semi-invariant polynomials of $A$ in terms of a canonically constructed basis that will be made precise in the text.
