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.



Question on a relation between minors of a particular kind of matrix
This must be a consequence od the Dodgson's condensation formula. See Exercise 24 on my web [site](http://www.umpa.ens-lyon.fr/~serre/DPF/exobis.pdf). By the way, C. L. Dodgson was the real name of Lewis Caroll (see the MO question [link text](https://mathoverflow.net/questions/45185).


