Let-A-R-N-N-be-a-symmetric-positive-definite-matrix-and-b-R-N-a-vector-If-x-R-N-evaluate-the-integral-Z-A-b-e-1-2-x-T-Ax-b-T-x-dx-as-a-function-of-A-and-b-

Question Number 203900 by necx122 last updated on 01/Feb/24

L e t A \in R^{N \times N} b e a s y m m e t r i c p o s i t i v e

d e f i n i t e m a t r i x a n d b \in R^{N} a v e c t o r .

I f x \in R^{N}, e v a l u a t e t h e i n t e g r a l

Z (A, b) = \int e^{- \frac{1}{2} x^{T} A x + b^{T} x} d x a s a f u n c t i o n

o f A a n d b .