Sum of matrices obtained as sum of vector products

Hello, I have a set of column vectors, organized in a matrix of size (number of vectors)x(length of vectors).

I need to construct a matrix as the sum of (number of vectors) matrices constructed from each vector as the product of the column vector times the vector transposed. DO you know any easy form to do this without a loop (which is very time consuming)? What I really need is the inverse of this matrix, but I guess there is no easy way to obtain it easyly.

Thank you very much in advance!

Ana

Answer 1

[Honglei Chen]

Hi Ana,

Let's say your matrix is X. If I understand correctly, each row of X is a vector you want and that vector suppose to be a column vector. If that is true I believe you are talking about forming sample covariance matrix. In your case, you can simply do it by

R = X'*X;

This being said, it is rare that you want to really invert R. In most cases, what you want is R^(-1)v where v being a vector. Hence, instead of using

inv(R)*v

you should do

R\v

HTH

[Ana]

Thank you very much! I knew there should be an easy way of doing this, but I couldn't realize how!

Yes, what I really need R^(-1)v, I posed the question in that way just in case it was simple to obtain the inverse of that matrix in an analytic way or something.

Thanks again!

Ana