Expected Value and covariance of matrix

[tommyhakinen]

I have a 2x1 matrix A. I would like to find out E[A] which is the mean of the matrix. How do I do this? what is the dimension of the resultant matrix? using this E[A], I am going to find the covariance of matrix A by this formula

cov(A) = E[(A - E[A])(A - E[A])$$^{T}$$)

could someone please enlighten me? thank you in advance.

 

[brydustin]

I have a 2x1 matrix A. I would like to find out E[A] which is the mean of the matrix. How do I do this? what is the dimension of the resultant matrix? using this E[A], I am going to find the covariance of matrix A by this formula

cov(A) = E[(A - E[A])(A - E[A])$$^{T}$$)

could someone please enlighten me? thank you in advance.

It depends on what you mean by the "mean of a matrix". I assume you are trying to find out what the elements of the matrix should be. Well if each element has a Gaussian distribution centered around 0, then the "average" vector should have all of its entries as 0. But this depends on your choice of distribution, mean for the element entries, and standard deviation.

Try to better define what you are saying

 

[brydustin]

I think you had better look at this:
http://www.itl.nist.gov/div898/handbook/pmc/section5/pmc541.htm
to get started.

 

[tommyhakinen]

I think you had better look at this:
http://www.itl.nist.gov/div898/handbook/pmc/section5/pmc541.htm
to get started.

Thanks for the reply. but if my matrix A is a 2x1 vector which only has two elements, is it possible to find the covariance or i have to have the set of data in order to get the covariance?

 

[blue_raver22]

I can provide some insight into expected value and covariance of a matrix. Expected value is a measure of the central tendency of a random variable, in this case, a matrix. It represents the average value of the matrix and is calculated by taking the sum of all the values in the matrix and dividing by the total number of values.

In order to find the expected value of a 2x1 matrix A, you would simply add the two elements in the matrix and divide by 2. The resultant matrix would have a dimension of 1x1, as it is a single value representing the mean of the matrix A.

Covariance, on the other hand, measures the relationship between two random variables. In this case, we are interested in finding the covariance of matrix A. The formula you have provided is correct. The covariance of matrix A is calculated by subtracting the expected value of A from each element in the matrix, multiplying them together, and then taking the average of all these values.

The resultant matrix of the covariance calculation would have a dimension of 2x2, as it represents the covariance between each element in the matrix A.

I hope this explanation helps to clarify the concepts of expected value and covariance in the context of a matrix. If you have any further questions, please don't hesitate to ask. Thank you.