# Relationship between the Eignevalues and Eigenvectors of Two Matrices

An assignment within my linear algebra class has us work on the basics of a facial recognition program.

One of the questions within the assignment defines a correlation matrix as 𝑪= 1/q(𝑴𝑴^T), where M is a previously defined matrix of size m x q.

It then asks for the relationship between eigenvalues and eigenvectors of 𝑪 and those of 𝑫=1/q𝑴^T𝑴.

I'm not exactly sure how to proceed with this question. I don't see a way to rewrite the equation represent the eigenvalues of C in terms of D or vice versa. I know that C will have m eigenvalues while D will have q eigenvalues, I just don't see how any more information can be obtained.

Thanks for any help.

• The expression $1/q^T$ doesn’t make much sense in this context. You say that $q$ is the number of columns of $M$, so $1/q$ is a scalar. – amd Apr 6 '17 at 2:56
• Possible duplicate of Non-zero eigenvalues of $AA^T$ and $A^TA$ – thanasissdr Apr 6 '17 at 3:33