Sign up ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let $Z \sim \mathcal{N}(0,\Sigma \otimes I)$ (so the columns of $Z$ are distributed $\mathcal{N}(0, \Sigma)$) and $A = Z'Z.$ Is there a name for the distribution on $A$? Is the density known?

share|cite|improve this question
If $Z'$ means the transpose, isn't this the Wishart distribution/density? – Yemon Choi Dec 4 '11 at 1:38
Oh, sorry, misread. So the columns are iid but the rows need not be? – Yemon Choi Dec 4 '11 at 1:45
Isn't this related to the: – Suvrit Dec 4 '11 at 10:52
I think I misunderstood the question. So is $Z$ a row vector of i.i.d. normals with mean zero and prescribed variance? – Yemon Choi Dec 5 '11 at 6:59
$Z$ is a matrix whose columns are distributed $\mathcal{N}(0, \Sigma).$ If the rows were distributed that way, then $Z'Z$ would be a Wishart distribution. – Alex Gittens Dec 5 '11 at 22:28

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.