| 关于域上无限方阵的逆方阵 |
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| 引用本文： | 王世强.关于域上无限方阵的逆方阵[J].北京师范大学学报(自然科学版),1993,29(3):327-330. |
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| 作者姓名： | 王世强 |
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| 作者单位： | 北京师范大学数学系 100875 |
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| 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.
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| 关 键 词： | 无限方阵 模型论 逆方阵 |
ON THE INVERSES OF INFINITE MATRICES ON A FIELD |
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| Wang Shiqiang.ON THE INVERSES OF INFINITE MATRICES ON A FIELD[J].Journal of Beijing Normal University(Natural Science),1993,29(3):327-330. |
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| Authors: | Wang Shiqiang |
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| Abstract: | 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. |
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| Keywords: | infinite matrix model theory inverse matrix |
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