Two-norm

English

Template:Lb A measure of length given by "the square root of the squares." Denoted by $| | \cdot | |_{2}$ , the two-norm of a vector $\vec{v} = < a_{1}, a_{2}, \dots, a_{n} >$ is $| | \vec{v} | |_{2} = \sqrt{a_{1}^{2} + a_{2}^{2} + \dots + a_{n}^{2}}$ . 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.