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You are not logged in. #1 20090328 09:41:49
Determinant of a Vandermonde matrixLast edited by JaneFairfax (20090328 23:31:32) #2 20090328 11:02:39
Re: Determinant of a Vandermonde matrixQuite fascinating Jane. That's the square root of the discriminant for a polynomial with roots a1, ..., an. Nice find. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #3 20090329 00:55:32
Re: Determinant of a Vandermonde matrixYes, it’s a nice find. By multiplying the ith row by and subtracting from the (i+1)th row we have By the inductive hypothesis, the determinant of the smaller matrix is . That completes the proof by induction. Last edited by JaneFairfax (20090329 01:33:49) #4 20090413 08:38:11
Re: Determinant of a Vandermonde matrixThe LHS is used by John E. Humphreys in A Course in Group Theory in the treatment of odd and even permutations. 