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

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SUMMARY

The covariance matrix for three vectors x, y, and z in MATLAB can be computed using the command cov(A), where A is a 3-row matrix containing the vectors. The covariance matrix is structured as follows: 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)]. This structure is confirmed to be correct, aligning with the mathematical definition of covariance, where each element (i,j) represents Cov(Xi, Xj).

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