Norm (mathematics) | Two norm
LengthinavectorspaceInmathematics,anormisafunctionfromarealorcomplexvectorspacetothenon-negativerealnumbersthatbehavesincertainwayslikethedistancefromtheorigin:itcommuteswithscaling,obeysaformofthetriangleinequality,andiszeroonlyattheorigin.Inparticular,theEuclideandistanceinaEuclideanspaceisdefinedbyanormontheassociatedEuclideanvectorspace,calledtheEuclideannorm,the2-norm,or,sometimes,themagnitudeofthevector.Thisnormcanbedefinedasthesquarerootoftheinnerproductofavectorwithitself.Aseminormsa...
Length in a vector space
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin. In particular, the Euclidean distance in a Euclidean space is defined by a norm on the associated Euclidean vector space, called the Euclidean norm, the 2-norm, or, sometimes, the magnitude of the vector. This norm can be defined as the square root of the inner product of a vector with itself.
A seminorm satisfies the first two properties of a norm, but may be zero for vectors other than the origin.[1] A vector space with a specified norm is called a normed vector space. In a similar manner, a vector space with a seminorm is called a seminormed vector space.
The term pseudonorm has been used for several related meanings. It may be a synonym of "seminorm".[1] A pseudonorm m...