Expected Value and covariance of matrix

[tommyhakinen]

I have a 2x1 matrix A. I would like to find out E[A] which is the mean of the matrix. How do I do this? what is the dimension of the resultant matrix? using this E[A], I am going to find the covariance of matrix A by this formula

cov(A) = E[(A - E[A])(A - E[A])^{T})

could someone please enlighten me? thank you in advance.

[brydustin]

I have a 2x1 matrix A. I would like to find out E[A] which is the mean of the matrix. How do I do this? what is the dimension of the resultant matrix? using this E[A], I am going to find the covariance of matrix A by this formula

cov(A) = E[(A - E[A])(A - E[A])^{T})

could someone please enlighten me? thank you in advance.


It depends on what you mean by the "mean of a matrix". I assume you are trying to find out what the elements of the matrix should be. Well if each element has a Gaussian distribution centered around 0, then the "average" vector should have all of its entries as 0. But this depends on your choice of distribution, mean for the element entries, and standard deviation.

Try to better define what you are saying

[brydustin]

I think you had better look at this:
http://www.itl.nist.gov/div898/handbook/pmc/section5/pmc541.htm
to get started.

[tommyhakinen]

I think you had better look at this:
http://www.itl.nist.gov/div898/handbook/pmc/section5/pmc541.htm
to get started.

Thanks for the reply. but if my matrix A is a 2x1 vector which only has two elements, is it possible to find the covariance or i have to have the set of data in order to get the covariance?