Common integrals in quantum field theory: Difference between revisions

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====Diagonalize the matrix====

The first step is to [[Diagonalizable matrix|diagonalize]] the matrix.<ref>{{cite book | author=Herbert S. Wilf| title=Mathematics for the Physical Sciences | publisher= Dover| year=1978 | isbn=0-486-63635-6| url-access=registration| url=https://archive.org/details/mathematicsforph0000wilf_w9m6}}</ref> Note that

:<math>A_{ij} x^i x^j \equiv x^TAx = x^T \left(OO^T\right) A \left(OO^T\right) x = \left(x^TO \right) \left(O^TAO \right) \left(O^Tx \right) </math>