How to calculate covriance between 2 coordinates set

If I have a set x which is a 10x2 matrix with each row as a coordinate (ie. there are 10 coordinates). And similarly I have another coordinate set y (10x2). How can I find the covariance between the two coordinate set? ie. One row should be considered as a single quantity. And I need to get a 10x10 covariance matrix which gives the covariance between each 10 coordinates.

Thanks in Advance.

[Aryan Ritwajeet Jha]

I don't think I got your question. What are your random variable vectors? Are they x and y? If yes, then the covariance matrix would be a 2x2 matrix.

A 10x10 covariance is only possilble if:

You specify x as a 2x10 matrix (i.e. there are 10 random variable vectors, each with two instances) and compute cov(x).

You specify y as a 2x10 matrix (i.e. there are 10 random variable vectors, each with two instances) and compute cov(y).

Note that if you specify both x and y as above and copute cov(x,y), you'll still get a 2x2 matrix as the random variable vectors are now x and y.

In all of the cases, it doesn't make sense. The only sensible covariance I can think of is taking the covariance between the x coordinates of data sets x and y, and similarly the covariance of the y coordinates of data sets x and y.

%initialize x and y each with ten coordinates  
x = randi(5,2,10);
y = randi(5,2,10);

%Three not very sensible covariance matrices:
%They are not sensible as the x and y coordinates of each
%data set is taken as an instance of the random variable
%even though they represent two different dimensions.
covXY = cov(x,y) %returns a 2x2 matrix
covX = cov(x) %returns a 10x10 matrix
covY = cov(y) %returns a 10x10 matrix

%Two sensible covariance matrices
covXY_x = cov(x(1,:),y(1,:)) %returns a 2x2 matrix
covXY_y = cov(x(2,:),y(2,:)) %returns a 2x2 matrix

[Nisha Varghese]

Hi,

Thanks for your comment.

My intention is to find out the difference between 2 coordinate sets.

For eg:,

X=[1 2;3 4;5 6] and Y=[1 3;3 3;5 5].

I want to find out whether the rows of X and Y are similar or how much variation is there between [1 2] & [1 3];

[3 4] & [3 3]; [5 6] & [5 5].

[Bjorn Gustavsson]

That would be:

dR = X-Y;

wouldn't it?

[Nisha Varghese]

Yes. It is a big matrix when the number of elements are high right?

I would like to get a similarity metric between 2 sets of coordinates.

ie., the deviation of tracked coordinates from the ground truth coordinates in Tracking of objects in image processing.