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Quadratic form is nover zero?

  1. Apr 29, 2015 #1
    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. smile.gif

    True or false? Why? If A is a real, symmetric, nonsingular matrix, then xTAx≠0 for x≠0.
     
  2. jcsd
  3. Apr 29, 2015 #2
    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.
     
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