Frobenius Norm

A way to measure the size/magnitude of a matrix.

It is calculated as the square root of the sum of the squares of all elements in a matrix.

$$=\sqrt{\sum _{i=1}^m\sum _{j=1}^n|a_{ij}{|}^2}$$

Example:

$$\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]:$$ $$=\sqrt{1^2+2^2+3^2+4^2}=\sqrt{1+4+9+16}=\sqrt{30}$$