矩阵空间之间的保幂线性映射

Power-Preserving Linear Maps between Matrix Spaces

中文关键词:  复数域  幂保持  线性映射.

英文关键词:complex field  power-preserving  linear map.

中文摘要:

      在本文中, 设$C$是复数域, $n$和$m$ 是正整数, $k$为固定的自然数, 且$k\geq 2$. 设$M_{m}(C)$为$C$上$m$ 阶全矩阵空间, $S_{n}(C)$为$C$上$n$ 阶对称矩阵空间. 本文分别刻画了从$S_{n}(C)$到$M_{m}(C)$和$S_{n}(C)$到$S_{m}(C)$上的保矩阵$k$次幂的线性映射.

英文摘要:

      Let $C$ be a complex field. Let $m$ and $n$ be positive integers. $k$ is a fixed positive integer and $k\geq 2$. Let $M_{m}(C)$ and $S_{n}(C)$ be the vector spaces of all $m\times m$ matrices and $n\times n$ symmetric matrices over $C$, respectively. We characterize the linear maps preserving $k$-power from $S_{n}(C)$ to $M_{m}(C)$ and $S_{n}(C)$ to $S_{m}(C)$, respectively.