英和和英

名詞

two-norm (複数形 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 ${\\displaystyle {\\vec {v}}=<a_{1},a_{2},\\ldots ,a_{n}>}$ 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.