Two-norm

Full definition of two-norm

Noun

1. Mathematical measure of length given by "the square root of the squares." Denoted by $||\backslash cdot||\_2$, the two-norm of a vector is $$

||\vec v||_2=\sqrt{a_1^2+a_2^2+\cdots+a_n^2}. The two norm of an $m\backslash times\; m$ matrix $A$ is defined by $\backslash max\_\{\backslash vec\; v\backslash neq\backslash vec\; 0\}\backslash frac\{||A\backslash vec\; v||\_2\}\{||\backslash vec\; v||\_2\}$ where $\backslash vec\; v$ is an m-dimensional vector that is not the zero vector.