Thread: help for an eigenvalue problem!

1. help for an eigenvalue problem!

I am wondering if somebody can be a help to solve this problem?

Let $\displaystyle A \in M_n[R]$, each row of $\displaystyle A$ has unit length,
and $\displaystyle A$ is nonsingular, how to prove that $\displaystyle A^T A$ which is SPD has all its eigenvalues less than 2?

Thanks for any help!

2. This assertion is wrong!

The problem stated above is actually not correct. Please forget about it!