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m Specify condition on matrix A: must be positive definite as to be invertible |
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:<math>\int \exp\left( - \frac 1 2 x \cdot A \cdot x +J \cdot x \right) d^nx = \sqrt{\frac{(2\pi)^n}{\det A}} \exp \left( {1\over 2} J \cdot A^{-1} \cdot J \right)</math>
Here {{mvar|A}} is a real positive definite [[symmetric matrix]].
This integral is performed by [[Diagonalizable matrix|diagonalization]] of {{mvar|A}} with an [[orthogonal matrix|orthogonal transformation]]
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