# The sample covariance of N observations of K

1. Sep 11, 2013

### DUET

http://en.wikipedia.org/wiki/Covariance

The sample covariance of N observations of K variables is the K-by-K matrix.

I am wondering-

Should "K-by-K" be "N-by-K" or not?

2. Sep 11, 2013

### mathman

No. K-by-K is correct. Moreover it is symmetric. Each term in the matrix is the estimated covariance between two of the variables.

3. Sep 11, 2013

### DUET

Does it mean covariance matrix must be in square size, 3x3, 4x4, 5x5 etc?

It can never be 3x4, 4x7, 5x8 etc.
Correct?

Last edited: Sep 12, 2013
4. Sep 12, 2013

### chiro

Yes it has to be square. Remember that you need all possible values of Cov(X,Y) where X and Y are random variables. If you have N different variables then you have N*N or N^2 possibilities and since Cov(X,Y) = Cov(Y,X) you will have a lot of repeated values.

5. Sep 12, 2013

### DUET

I think every value will repeat twice. Am I correct?

6. Sep 12, 2013

### chiro

In general yes unless you are looking at the same random variable since Cov(X,X) = Var(X) on the diagonal elements.

7. Sep 12, 2013

### DUET

Yes! I am just taking off diagonal elements into account.

Last edited: Sep 12, 2013