- #1

jarra

- 9

- 0

## Homework Statement

The task is to show that the eigenvalues of overlap matrix [tex]\tilde S[/tex] are positive.

## Homework Equations

The overlap matrix is defined as [tex] (\tilde S)_{nm} = \langle \xi_n \vert \xi_m \rangle [/tex], with [tex]\xi_k[/tex] being the base vectors of the wavefunction. http://en.wikipedia.org/wiki/Overlap_matrix

## The Attempt at a Solution

I've tried to show that the eigenvalues are positive by showing that [tex]\tilde S[/tex] is positive definite. Both with the condition [tex]\vec x^{\ast} \tilde S \vec x > 0[/tex] and the condition that all the 'sub-determinants' are larger than zero. But I don't get it right, please help.