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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.
  • [1] {1}

    BOURQUE K, LIGH S. On GCD and LCM matrices[J]. Linear Algebra Appl,

    1992, 174: 65-74.
    {2}

    CAO W. On Hong's conjecture for power LCM matrices[J]. Czechoslovak

    Math J, 2007, 57: 253-268.
    {3}

    HONG S. On the Bourque-Ligh conjecture of least common multiple

    matrices[J]. J Algebra, 1999, 218: 216-228.
    {4}

    HOGN S. Gcd-closed sets and determinants of matrices associated with

    arithmetical functions[J]. Acta Arith, 2002, 101: 321.
    {5}

    HOGN S. Nonsingularity of matrices associated with classes of

    arithmetical functions[J]. J Algebra, 2004, 281: 1-14.
    {6}

    HOGN S. Divisibility properties of power GCD matrices and power LCM

    matrices[J]. Linear Algebra Appl, 2008, 428: 1001-1008.
    {7}

    HOGN S, LEE Enoch K S. Asymptotic behavior of eigenvalues of

    reciprocal power LCM matrices[J]. Glasgow Math J, 2008, 50(1):

    163-174.
    {8}

    HOGN S, LOEWY R. Asymptotic behavior of eigenvalues of greatest

    common divisor matrices[J]. Glasgow Math J, 2004, 46: 551-569.
    {9}

    HOGN S, LOEWY R. Asymptotic behavior of the smallest eigenvalue of

    matrices associated with completely even functions (mod r)[J].

    International J, Number Theory, 2011, 7: 1681-1704.
    {10}

    LIN Z, TAN Q. Determinants of Smith matrices on three coprime

    divisor chains and divisibility[J]. Linear Multilinear Algebra,

    2012, 60: 475-486.
    {11}

    LIN Z, TAN Q. Nonsingularity of reciprocal power GCD matrices and

    reciprocal power LCM matrices on two quasi-coprime divisor

    chains[J]. J Sichuan Univ Nat Sci Ed, in press.
    {12}

    SMITH H J S. On the value of a certain arithmetical determinant[J].

    Proc London Math Soc, 1875-1876, 7: 208-212.
    {13}

    TAN Q. Divisibility among power GCD matrices and among power LCM

    matrices on two coprime divisor chains[J]. Linear Multilinear

    Algebra, 2010, 58: 659-671.
    {14}

    XU J, LI M. Divisibility among power GCD matrices and among power

    LCM matrices on three coprime divisor chains[J]. Linear Multilinear

    Algebra, 2011, 59: 773-788.
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  • 被引次数: 0
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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