0
$\begingroup$

Let $\sigma$ be the Lebesgue measure on the unit sphere $\mathbb S^{n-1}$ of $\mathbb R^n$.

Let $\Sigma$ be a semi-definite positive symmetric matrix in dimension $n$.

Is it possible to get a closed-form expression for the following integral:

$$\int_{u \in \mathbb S^{n-1}} \left(u'\Sigma u\right)^{\frac 12} \ \sigma(du)$$

$\endgroup$
1
  • $\begingroup$ Is $u'$ meant to be $u^T$ (ie. the transpose)? Would you know how to do it if $\Sigma$ was diagonal (I guess one can just make a change of variables to diagonalize our matrix, but I do not quite see how to do the diagonal case)? $\endgroup$
    – Severin Schraven
    Commented Jun 17 at 21:39

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .