bound on eigenvalues...

Hi all,

Given a matrix

A =

0.1337 0.1115 0.1647
0.1115 0.1584 0.1362
0.1647 0.1362 0.2089

I know by numerical computation that its eigenvalues are:

ans =

0.0023
0.0513
0.4475

so any number > 0.4475 is the bound on the eigenvalues...

But how do I find bound analytically?

Can I prove that the eigenvalues are less than a number, say, 0.8, or
0.9, or x, where x<1 strictly analytically?

.