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定义在三个拟互素因子链上的倒数幂矩阵的非奇异性

罗淼 谭千蓉

罗淼, 谭千蓉. 定义在三个拟互素因子链上的倒数幂矩阵的非奇异性[J]. 华东师范大学学报(自然科学版), 2013, (3): 164-168,175.
引用本文: 罗淼, 谭千蓉. 定义在三个拟互素因子链上的倒数幂矩阵的非奇异性[J]. 华东师范大学学报(自然科学版), 2013, (3): 164-168,175.
LUO Miao, TAN Qian-rong. Nonsingularity of the reciprocal power matrices on three quasi-coprime divisor chains[J]. Journal of East China Normal University (Natural Sciences), 2013, (3): 164-168,175.
Citation: LUO Miao, TAN Qian-rong. Nonsingularity of the reciprocal power matrices on three quasi-coprime divisor chains[J]. Journal of East China Normal University (Natural Sciences), 2013, (3): 164-168,175.

定义在三个拟互素因子链上的倒数幂矩阵的非奇异性

详细信息
  • 中图分类号: O156.1

Nonsingularity of the reciprocal power matrices on three quasi-coprime divisor chains

  • 摘要: 首先给出定义在三个拟互素因子链上的倒数幂~GCD~矩阵和倒数幂~LCM 矩阵的行列式的计算公式, 由此证明定义在三个拟互素因子链~$S$~上且~$S$ 的最大公因子属于~$S$~时的倒数幂~GCD~矩阵和倒数幂~LCM~矩阵是非奇异的. 但当构成~$S$~的三个因子链不素时, 如此的结果不成立.
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出版历程
  • 收稿日期:  2012-06-01
  • 修回日期:  2012-09-01
  • 刊出日期:  2013-05-25

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