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A useful fact on x^T*A*x

27/04/2011

Useful: x^TAx=\Sigma_{i,j}^{n}A_{ij} x_i x_j.

Brief proof: A=[a_1,a_2,...,a_n]. Then

x^TA=[\Sigma_{i}x_i a_{i1},\Sigma_{i}x_i a_{i2},..., \Sigma_{i}x_i a_{in}]

So x^TAx=\Sigma_{i}x_i a_{i1} x_1+\Sigma_{i}x_i a_{i2}x_2 + ...+ \Sigma_{i}x_i a_{in}x_n=\Sigma_{i,j}^{n}A_{ij} x_i x_j

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