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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 |
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inequality for a symmetric nonnegative matrixGiven 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
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