I know that covariance matrix represent data as eigenvector of it but I want to understand how could covariance matrix represent data mathematically?
How could those values help for representing some kind of average of data?
Multiplying any random vector repeatedly with covariance matrix results in the eigenvector (some scale of it) but how? (I try for a 2d vector space with x and y values and get some equations but I could not prove it.) Could we prove that the covariance matrix represent the data geometrically or in mathematical sense?