Understanding the “computationally convenient uniqueness condition” of factor model

#1
In the book "Applied Multivariate Statistical Analysis" written by Johnson and Wichern, they have mentioned about a computationally convenient uniqueness condition $L^T\psi^{-1}L=\Delta$, where $\Delta$ is a diagonal matrix. Here, $L$ is the factor loadings matrix and $\psi$ is vector of specific variances.

I cannot understand how this condition removes the multiple choices of $L$ and makes it unique. Can anyone help?