# What is the difference between covariance matrix and the variance-covariance matrix?

What is the difference between covariance matrix and the variance-covariance matrix?

I am bit unsure whether there exists any difference at all. Google tells me that variance-covariance matrix is the matrix where the variance is written in the diagonal of the matrix, and the other elements are covariances between the variables. But isn't it the same for the covariance matrix?

• Yes, they are the same thing. – ATJ Dec 28 '15 at 16:44
• ......Why can't they just use one word to describe it... – Bob Burt Dec 28 '15 at 16:46
• They can, and often use just "covariance matrix". Saying "variance-covariance" reminds a reader the fact that the notion of variance is alias to covariance, the co-variance of a variable with own self. – ttnphns Dec 28 '15 at 16:55
• "......Why can't they just use one word to describe it..."; there's probably not a single statistical method that this quote cannot be applied to. A side result of statistical methods being applied to different areas of study – Cliff AB Dec 28 '15 at 19:07
• Here is a somewhat related thread on Meta CV. – Richard Hardy Dec 29 '15 at 9:26

In such matrices, you find variances (on the main diagonal) and covariances (on the off-diagonal). So variance-covariance matrix is completely fine, but a bit redundant as a variance is a special Kind of covariance ($Var(X) = Cov(X, X)$). So covariance matrix is also correct - while beeing shorter.