# Quadratic form is nover zero?

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1. Apr 29, 2015

### elimax

Basic question, I think, but I'm not sure. It is a step in a demonstration, so it would be nice if it were true.

True or false? Why? If A is a real, symmetric, nonsingular matrix, then xTAx≠0 for x≠0.

2. Apr 29, 2015

### Truecrimson

Since $A$ is real and symmetric, it is diagonalizable. So you may start by thinking about $x^T A x$ in a basis in which $A$ is diagonal.