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Definition 2024

two-norm ‎(plural two-norms)

Mathematical measure of length given by "the square root of the squares." Denoted by $||\cdot ||_{2}$ , the two-norm of a vector ${\vec {v}}=<a_{1},a_{2},\ldots ,a_{n}>$ 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.

mathematical measure of length