In the notes I'm working through the following is said:
The eigenvalue decomposition of a matrix A, is $A=U\Lambda U^T$.
Later in the notes, it's said that "if A is multiplied with U we immediately see that $\Lambda$ contains the eigenvalues since $AU=\Lambda U$
I understand that by definition $\Lambda$ is the matrix of eigenvalues but how do we immediately see that $\Lambda$ contains the eigenvalues since $AU=\Lambda U$? At the moment I don't really see the significance of this statement.