If the matrix $A$ contains only real values and is also symmetric, then the spectral radius of $A^TA$ is:
$$ \rho(A^TA)= (|\lambda|_{max})^2 \tag1$$
where $|\lambda|_{max}$ is the maximum absolute eigenvalue of matrix $A$. In my case, I am trying to find the spectral radius of $A^TA$ where $A$ is not symmetric. Is there any way I can do this without actually multiplying $A^T$ and $A$? The format of $A$ is quite big, so it is not very practical. Note that the elements of any of its diagonals are the same. For example:
$$A = \begin{bmatrix} a & b & 0 & c & 0 \\ d & a & b & 0 & c \\ 0 & d & a & b & 0 \\ e & 0 & d & a & b \\ 0 & e & 0 & d & a \end{bmatrix} \tag 2$$