Re: The determinant of a matrix
- From: "Chip Eastham" <hardmath@xxxxxxxxx>
- Date: 7 Nov 2006 13:43:18 -0800
Yecloud wrote:
Hi, all,
I have a question on calculating the determinant of a matrix and am
wondering if there is any well-known formula for it. The matrix is in
K-by-K dimension and symmetric, the entry at (i,j) is a^((i-j)^2),
where
a >0 and a < 1.
The type of matrix you ask about is of a special form, having
the same value along entries in each "subdiagonal". The name
for these specially formed matrices is a Toeplitz matrix.
There are "fast" algorithms available for these, and in particular
the determinant can be calculated in O(n^2) operations. It's
possible that there is a closed form expression for these, but
I'll have to think about it.
Meanwhile you might want to Google for "Toeplitz determinant"
and see if something strikes you as algorithmically usable.
regards, chip
.
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