2 prettified with LaTeX

Given A $A$ symmetric and semidefinite positive, for each x $x$ $$x'Ax >= 1/||A|| ||Ax||^2\geq \frac{1}{\Vert A\Vert} \Vert Ax \Vert^2$$

This inequality appears at page 24 of "Introduction to Optimization" from Boris T. Polyak. I haven't been able to prove it. Any idea?

Thanks, Giovanni

1

inequality for a symmetric nonnegative matrix

Given A symmetric and semidefinite positive, for each x x'Ax >= 1/||A|| ||Ax||^2

This inequality appears at page 24 of "Introduction to Optimization" from Boris T. Polyak. I haven't been able to prove it. Any idea?

Thanks, Giovanni