# two-norm

1. 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 $m\times m$ matrix $A$ is defined by $\max_{\vec v\neq\vec 0}\frac{||A\vec v||_2}{||\vec v||_2}$ where $\vec v$ is an m-dimensional vector that is not the zero vector.