Why covariance matrix is computed like this?

Question

Wenlong 2012-8-31

Hi, all

I know am asking a quite fundamental question, but I really can't remember the answer that my teacher taught me in class.

Let A be a matrix has m rows and n columns, the covariance matrix C is computed as follows

C = (AT)(A)/(m-1)

where (AT) is the transpose of A.

My question is, why it is divided by (m-1)? I remember it also can be divided by m, and it is all about sample size or something....

Can anyone help me to answer this question? Many thanks for your kindly help.

Best regards Wenlong

Walter Roberson 2012-8-31

I believe it is a "degrees of freedom" issue.

Answer 1

Ilya 2012-8-31

m-1 in the denominator gives the unbiased estimate, and m gives the max likelihood estimate.