The eigenvalue of $A^TA$ If $\lambda$ is the eigenvalue of matrix $A$,what is the eigenvalue of $A^TA$?I have no clue about it. Can anyone help with that?

Generally, you won't be able to say much about them.
However, if $A$ is for instance real symmetric, it is diagonalizable with real eigenvalues, meaning there is an orthogonal matrix B (that is with $B^{-1}=B^T$) and a diagonal matrix D such that:
$$A = B D B^T$$
$$A^TA = (B D B^T)^T B D B^T = B D^T B^T B D B^T = BD^2B^T$$
In other words, the eigenvalues of $A^TA$ are the squares of the eigenvalues of $A$.
