# two-norm

## EnglishEdit

### NounEdit

two-norm ‎(plural two-norms)

1. Mathematical measure of length given by "the square root of the squares." Denoted by ${\displaystyle ||\cdot ||_{2}}$ , the two-norm of a vector ${\displaystyle {\vec {v}}=}$  is ${\displaystyle ||{\vec {v}}||_{2}={\sqrt {a_{1}^{2}+a_{2}^{2}+\cdots +a_{n}^{2}}}}$ . The two norm of an ${\displaystyle m\times m}$  matrix ${\displaystyle A}$  is defined by ${\displaystyle \max _{{\vec {v}}\neq {\vec {0}}}{\frac {||A{\vec {v}}||_{2}}{||{\vec {v}}||_{2}}}}$  where ${\displaystyle {\vec {v}}}$  is an m-dimensional vector that is not the zero vector.