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Raxel
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Distribution of quadratic form of multivariate normal with linear term

Suppose that $A$ is a symmetric non-random matrix and $X\sim N(\mu,\Sigma)$ and $b \in R^n$ is a non-random vector. Then what is the distribution of $$X^tAX+b^tX \quad ?$$

The distribution without the linear term is solved in the answer here(Transformation of multivariate normal sum of chi-squared) but I have not solved the problem to the more general question above.

Raxel
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