摘要
用紧致性论证给出了任一域K上行列有限的无限方阵A具有各种逆方阵的基本的充分必要条件.主要结果是:A在K上具有唯一的行列有限双侧逆方阵当且只当A的各行向量在K上无限线性无关并且各列向量也在K上无限线性无关.
Some basic necessary and sufficient conditions for the existence of various inverses of a row-column-finite infinite matrix A over a field K are proved by compactness arguments. The main result is as follows: A ha an unique row-column- finite inverse on K if and only if the row-vectors of A are infinitely linearly independent on K and also the column-vectors of A are infinitely linearly independent on K.
出处
《北京师范大学学报（自然科学版）》
CAS
CSCD
1993年第3期327-330,共4页
Journal of Beijing Normal University(Natural Science)
基金
国家教委博士点基金
关键词
无限方阵
模型论
逆方阵
infinite matrix
model theory
inverse matrix
