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Pascal矩阵的一种显式分解 总被引:2,自引:0,他引:2
本文引入了两种广义Pascal矩阵凡,Pn,k,Qn,k以及两种广义Pascal函数矩阵On,k[x,y],Qn,k[x,y],证明了Pascal矩阵能够表示成(0,1)-Jordan矩阵的乘积而且Pascal函数矩阵能分解成双对角矩阵的乘积. 相似文献
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本文研究了Pascal矩阵与位移Pascal矩阵之间的关系.利用组合恒等式与矩阵分解的方法,得到了Pascal矩阵以及位移Pascal矩阵与若当标准型之间的过渡矩阵.同时也得到了这两类矩阵在域Zp上的最小多项式. 相似文献
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Lowell Abrams Donniell E. Fishking Silvia Valdes-Leon 《Linear and Multilinear Algebra》2000,47(2):129-136
Let B denote either of two varieties of order n Pascal matrix, i.e., one whose entries are the binomial coefficients. Let BR denote the reflection of B about its main antidiagonal. The matrix B is always invertible modulo n; our main result asserts that B-1 ≡ BR mod n if and only if n is prime. In the course of motivating this result we encounter and highlight some of the difficulties with the matrix exponential under modular arithmetic. We then use our main result to extend the "Fibonacci diagonal" property of Pascal matrices. 相似文献
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Lowell Abrams Donniell E. Fishking Silvia Valdes-Leon 《Linear and Multilinear Algebra》2013,61(2):129-136
Let B denote either of two varieties of order n Pascal matrix, i.e., one whose entries are the binomial coefficients. Let BR denote the reflection of B about its main antidiagonal. The matrix B is always invertible modulo n; our main result asserts that B-1 ≡ BR mod n if and only if n is prime. In the course of motivating this result we encounter and highlight some of the difficulties with the matrix exponential under modular arithmetic. We then use our main result to extend the "Fibonacci diagonal" property of Pascal matrices. 相似文献
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S. H. Dalalyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2008,43(5):274-284
The present paper gives a direct proof of the following result: for any linear operator over arbitrary field there exists a basis in which it has a polyquasicyclic matrix, i.e. a generalized Jordan form of second kind. The polyquasicyclic form of a linear operator is uniquely determined up to the order of direct summands on the diagonal, and it is shown that the generalized Jordan form of second kind is a link that connects the classical Jordan form and the rational canonical form. 相似文献
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将求解一般0-1策略对策的完全混合Nash均衡的问题转化为求解根为正的纯小数的高次代数方程组的问题.作为一种特殊而重要的情形,利用Pascal矩阵,Newton矩阵(对角元素为Newton二项式系数的对角矩阵)和Pascal-Newton矩阵(Pascal矩阵和Newton矩阵的逆阵的乘积)将求解对称0-1对策的完全混合Nash均衡的问题转化为求解根为正的纯小数的高次代数方程的问题,并给出第二问题的反问题(由完全混合Nash均衡求解对称0-1对策族)的求解方法.同时,给出了一些算例来说明对应问题的算法. 相似文献