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A note on LU decomposition of the Discrete Fourier Transform matrix | | Alexey Kuznetsov
; | | Date: |
2 Jul 2015 | | Abstract: | We describe some properties of the lower triangular Toeplitz matrix $T_q$
with coefficients $t_{i,j}=1/(q;q)_{i-j}$, where $(z;q)_k$ is the q-Pochhammer
symbol. We identify explicitly the inverse of $T_q$ and show that both this
matrix and its transpose appear in LU decomposition of the Vandermonde matrix
$V_q$ having coefficients $v_{i,j}=q^{ij}$. When $q$ is the $n$-th root of
unity, our result gives an explicit LU decomposition of the Discrete Fourier
Transform matrix. | | Source: | arXiv, 1507.2959 | | Services: | Forum | Review | PDF | Favorites | |
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