Let be given numbers. Compute the determinant of the nxn matrix , where .

I don't understand what is meant by this:

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- Sep 26th 2011, 02:51 PMdwsmithDeterminant
Let be given numbers. Compute the determinant of the nxn matrix , where .

I don't understand what is meant by this: - Sep 26th 2011, 02:57 PMDevenoRe: Determinant
without being given any more context, i would assume it means is the (i-1)-th power of . so the first row should all be 1's. this kind of matrix is called a Vandermonde matrix.

you'll probably arrive at a better understanding if you try it first for n = 2, and n = 3. try to factor the result into binomials.

if you are clever, and figure out (guess) the general form, you can actually prove it by induction on n. - Sep 26th 2011, 03:02 PMdwsmithRe: Determinant
- Sep 26th 2011, 03:08 PMpickslidesRe: Determinant
I see it as

- Sep 26th 2011, 03:08 PMDevenoRe: Determinant
well it's an important matrix, both for the study of polynomials, alternating bilinear forms, and permutation groups. it crops up in a lot of different places. time to roll up your sleeves and make some messy calcs...lol

@pickslides: i don't think so....there's nothing in the wording to indicate membership. and the calculation of such a determinant (a Vandermonde matrix) is the sort of thing you might encounter in a variety of different courses, inclusing differential geometry, linear algebra and group theory. i think the first time i saw it was in a physics class. - Sep 26th 2011, 03:12 PMdwsmithRe: Determinant
- Sep 26th 2011, 03:22 PMDevenoRe: Determinant

does it look better written out like this? - Sep 26th 2011, 03:28 PMdwsmithRe: Determinant
- Sep 26th 2011, 03:48 PMDevenoRe: Determinant
fair enough. but perhaps if someone else peruses this thread one day, it will be helpful to them. no slight intended.