Symmetric functions and the Vandermonde matrix
Symmetric functions and the Vandermonde matrix
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DOI：
10.1016/j.cam.2004.01.032
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发表时间：
2004-11
影响因子：
2.4
通讯作者：
H. Oruç;H. Akmaz
中科院分区：
文献类型：
--
作者：
H. Oruç;H. Akmaz
本文利用对称函数和组合恒等式推导了范德蒙矩阵逆的上三角因子和下三角因子。L和U矩阵又被分解为双对角矩阵。递归地求出了范德蒙矩阵及其逆矩阵中的上三角矩阵的元素。研究了范德蒙矩阵的不定式中的特殊值xi=1+q+ xi +qi− 1，并由此导出了q-二项式矩阵和q-斯特林矩阵。它还表明，q-斯特林矩阵可以得到从帕斯卡矩阵。
This work deduces the lower and the upper triangular factors of the inverse of the Vandermonde matrix using symmetric functions and combinatorial identities. The L and U matrices are in turn factored as bidiagonal matrices. The elements of the upper triangular matrices in both the Vandermonde matrix and its inverse are obtained recursively. The particular value xi=1+q+⋯+qi−1in the indeterminates of the Vandermonde matrix is investigated and it leads to q-binomial and q-Stirling matrices. It is also shown that q-Stirling matrices may be obtained from the Pascal matrix.