# The sample covariance of N observations of K

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?

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

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:
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.

1 person
you will have a lot of repeated values.
I think every value will repeat twice. Am I correct?

chiro