# How to find covariance matrix of 3 or more vectors in matlab?

1. Aug 16, 2013

### dexterdev

Hi all,
I know how to find covariance of 2 vectors and variance too. If covariance matrix is to be found of 3 vectors x,y and z, then then the cov matrix is given by

cov_matrix(x,y,z) =[var(x) cov(x,y) cov(x,z); cov(x,y) var(y) cov(y,z); cov(x,z) cov(y,z) var(z) ];

Is this equation right? In matlab I believe we first have to define a 3 row matrix 'A' to consider 3 vectors at once finding covariance matrix. Then command cov(A) gives the cov matrix. But I doubt whether this result matches with the above equation.

-Devanand T

2. Aug 16, 2013

### chiro

Hey dexterdev.

In general, the covariance matrix element (i,j) has the value Cov(Xi,Xj) = E[Xi*Xj] - E[Xi]E[Xj] for all random variables Xi and Xj. If i = j you get the variance Var[Xi].

This definition holds for any finite number of random variables.

3. Aug 16, 2013

### dexterdev

@chiro : I got it Sir, thanks....

Last edited: Aug 17, 2013