4.9a Frobenius Norm

Frobenius Norm

The Frobenius norm of a matrix $A\in {\mathbb{R}}^{m\times n}$ is the sum-of-squares of its diagonals, such that
$||A|{|}_F=\sqrt{{\sum }_{i=1}^m{\sum }_{j=1}^n|A_{ij}{|}^2}=\sqrt{\mathrm{Tr}(A^{T}A)}.$