Re: derivatives and determinant

On Mon, 13 Mar 2006 02:40:55 EST, eugene <jane1806@xxxxxxx> wrote:

Let f(x)=(x-x_1)(x-x_2)...(x-x_n)where the numbers x_1,x_2,...,x_n-pairwise distinct and a_{ii}=f''(x_i), a_{ij}=(f(x_i)-f(x_j))/(x_i-x_j).
What information we can say about such a matrix Can we say that detA=0 ?

No.

For example, try it with n=2 and any choice of distinct numbers x_1,
x_2.

Did you even try an example?

Also, can you see that, in all cases, the matrix A must be a diagonal
matrix?

quasi
.