What is "two-norm"

n. Mathematical measure of length given by "the square root of the squares." Denoted by $||cdot||\_2$, the two-norm of a vector $vec\; v=$ is $||vec\; v||\_2=sqrt\{a\_1^2+a\_2^2+cdots+a\_n^2\}$. The two norm of an $mtimes\; m$ matrix $A$ is defined by $max\_\{vec\; vneqvec\; 0\}frac\{||Avec\; v||\_2\}\{||vec\; v||\_2\}$ where $vec\; v$ is an m-dimensional vector that is not the zero vector.