frobenius norm

• the matrix trace is related to the frobenius norm:

\[||A||^2 = Tr(A^TA) = \langle Vec(A), Vec(A) \rangle\]

• The way to see this is to see that the trace is the sum of the diagonal elements. And the first element of the diagonal of \(A^TA\) is the first column vector dotted with itself. And the second element is the second column vector dotted with itself and so on.