The norm of an $m\times n$-matrix $A$ is defined as $\displaystyle ||A||^2 =  \textrm{tr}(A^t A) = \sum_{i,j} a_{ij}^2$. It stays the same if we multiply $A$ from the left or from the right by an orthogonal matrix $R$: $||RA||^2 =\textrm{tr}((RA)^t(RA)) … Continue reading The cotan formula