Why can not the vector be transposed in integrating over a region?

Question

Clear[x, A];
A = {{2, -1, 0}, {-1, 2, -1}, {0, -1, 1}};
Integrate[Exp[-x.A.{x}\[Transpose]/2], x \[Element] FullRegion[3]]

This code raises an error

Transpose::nmtx: "The first two levels of {x} cannot be transposed."

How can I fix it?

For 1D lists you don't actually need to transpose but most importantly you don't want to use curly braces. Just (x.A.x)/2 will work. — b.gates.you.know.what, Aug 02 '15 at 06:50
A discussion why the concept of row and column vectors are not needed can be found here. — Sjoerd C. de Vries, Aug 02 '15 at 07:03

score 3 · Answer 1 · answered Aug 02 '15 at 06:57

3

Perhaps what you are looking for is:

A = {{2, -1, 0}, {-1, 2, -1}, {0, -1, 1}};
Integrate[Exp[(-x . A . x)/2], x ∈ FullRegion[3]]

2 Sqrt[2] π^(3/2)

answered Aug 02 '15 at 06:57

m_goldberg

1 Answers1