two-norm
التعريفات والمعاني
== English ==
=== Noun ===
two-norm (plural two-norms)
(mathematics) A measure of length given by "the square root of the squares." Denoted by
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{\displaystyle ||\cdot ||_{2}}
, the two-norm of a vector
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=<
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,
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>
{\displaystyle {\vec {v}}=<a_{1},a_{2},\ldots ,a_{n}>}
is
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=
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⋯
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{\displaystyle ||{\vec {v}}||_{2}={\sqrt {a_{1}^{2}+a_{2}^{2}+\cdots +a_{n}^{2}}}}
. The two norm of an
m
×
m
{\displaystyle m\times m}
matrix
A
{\displaystyle A}
is defined by
max
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≠
0
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A
v
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2
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v
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{\displaystyle \max _{{\vec {v}}\neq {\vec {0}}}{\frac {||A{\vec {v}}||_{2}}{||{\vec {v}}||_{2}}}}
where
v
→
{\displaystyle {\vec {v}}}
is an m-dimensional vector that is not the zero vector.
==== Translations ====