# Question on a relation between minors of a particular kind of matrix

Hi!

Perhaps it is an easy question but i don't figure out how to prove it. Let $a_1,...,a_{2m+2}\in\mathbb{C}$ and for $1\leq i\leq 2m+2$ and $j\leq [\frac{2m+2-i}{2}]$ (with $[a]$ i mean the integer part of $a$) consider the matrix $A(i,j)=(a_{i+k+l})_{0\leq k,l\leq j}$. I denote with $D(i,j)=\det(A(i,j))$. I have to prove the following relation:$$D(1,m-1)D(3,m-1)-D(1,m)D(3,m-2)=D(2,m-1)^2$$

I tried by induction but i didn't manage to get the result.

Any help or hint would be appreciated.

Thank you in advance.

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First : did you try in low dimension, to get a feel of the problem. Second : is it homework you want done? –  Julien Puydt Feb 3 '11 at 15:53
@Snark: yes i tried in low dimension and the result is correct, i didn't find this relation as an exercise or homework but in an article i'm reading. It is said "well known identity on determinants" so i tried to prove it because i didn't know that identity. –  Italo Feb 3 '11 at 17:39