I know there are plenty of questions regarding 2 matrices one is [T]BB and one is [T]EE , so we all know that eigenvalues and eigenvectors are kept across different bases.
My question is what happens when you have a transformation from one basis to another are the eigenvalues kept the same ?
For example i have one matrix that gets vectors relative to base B and the image is returned according to base E would its eigenvalues be exactly the same as the same transformation from E to E?