Matlab Co-variance matrix

Question

I have two signals X : [250x1] double and Y : [250x1] double,

I want to calculate the co-variance matrix, by the deffinition.

The answer should be C : [250x250] double. However by C = cov(X,Y),

the answer is C : [2x2] double.

What is the problem?

I want to calculate (X-mean(X))T * C^-1 * (Y-mean(Y)),

which faces problem with a C : [2x2] double.

well according to your link (last line of the intro): "a 2×2 matrix would be necessary to fully characterize the two-dimensional variation." so everything looks fine no? — Ben
– Ben, Commented Oct 20, 2014 at 12:32
What does X mean? Is X a multidimensional process or are the rows of X realizations of the same process? (same for Y) — gire
– gire, Commented Oct 20, 2014 at 12:33
@Benoit_11, I want to calculate (X-mean(X))T*C^-1*(Y-mean(Y)), so C should be [250*250] for it to work. — Rash
– Rash, Commented Oct 20, 2014 at 12:37
@NKN, cov(x,y) returns the conariance matrix of x and y according to MATLAB help. — Rash
– Rash, Commented Oct 20, 2014 at 12:38

NKN · Accepted Answer · 2014-10-20 12:45:05Z

In many applications, the concept of covariance is like the variance, but applied to a comparison of two vectors: in place of the sum of squares, we have a sum of cross-products.

According to your comment:

I want to calculate (X-mean(X))TC^-1(Y-mean(Y)),

I guess you are looking for something like the following:

X=randn(250,1); Y=randn(250,1); C = (1/249)*(X-mean(X))'*(Y-mean(Y))

It has been divided by N-1 to get an unbiased estimator of the sample covariance.

Also, if you want to comapre two matrices using cov function, you may do this:

X = randn(250,1); Y = randn(250,1); C = cov([X(:) Y(:)]) % the result is a 2x2 matrix

could you please check this to see that if your formula would work in that pdf eq.(2.4), thanks
finally I used your formula and it worked, but I'm not sure if it's true!

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