definite positive symmetric bilinear form

Question

Let A be the matrix of a positive definite symmetric bilinear form.

Prove ִִ$a_1,$$_1$$a_n,$$_n$≥$a$$_1,$$_n$$a_n,$$_1$

I dont really have any idea what to do here.

Answer 1

If $A$ is the matrix of a positive definite symmetric bilinear form $\langle \cdot,\cdot\rangle$ with respect to basis $(e_1,\dots, e_n)$, then $a_{11}=\langle e_1,e_1\rangle$, $a_{nn}=\langle e_n,e_n \rangle$ and $a_{n1}=a_{1n}=\langle e_1,e_n\rangle$. The inequality is just an application of Cauchy-Schwarz inequality.