Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $X = (X_1,...,X_n)$ and $Y=(Y_1,...,Y_m)$ be two random vectors. Let $C_{XY}$ be the covariance matrix of two random vectors $X$ and $Y$.

What is the interpretation of the matrix $A = C_{XX}^{-1/2} C_{XY} C_{YY}^{-1/2}$?

It seems to me like it is very much related to the correlation matrix, but it is not exactly a correlation matrix (because its elements are actually not $Corr(X_i,X_j)$).

However, if $m=n=1$, then we get that $A$ is exactly a 1 x 1 matrix that corresponds to the correlation between $X$ and $Y$.

share|cite|improve this question

1 Answer 1

The variance-covariance matrix of $\tilde X=C_{XX}^{-1/2}X$ is the identity matrix $I_n$. The variance-covariance matrix of $\tilde Y=C_{YY}^{-1/2}Y$ is the identity matrix $I_m$. The covariance matrix of $\tilde X$ and $\tilde Y$ is the matrix $A$.

share|cite|improve this answer

Your Answer


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

Not the answer you're looking for? Browse other questions tagged or ask your own question.