Consider a square matrix $A$, and from it construct $B$ whose entries are the squared magnitudes of those in $A$. What can we say about the spectral radius of $B$? I know that for a unitary matrix $A$, $B$ is unistochastic so its spectral radius is 1, but I'm interested in the general case for arbitrary $A$.
Also, relatedly, for general $A$, what can be said of the column 1-norms of $B$? And what about the the column 1-norms of products of such $B$-type matrices?