(Untitled) (Untitled)(Untitled) (Untitled)(Untitled) (Untitled)(Untitled) (Untitled)(Untitled)Examples




IEVref:102-03-04ID:
Language:enStatus: Standard
Term: vector, <mathematics>
Synonym1:
Synonym2:
Synonym3:
Symbol:
Definition: element of a vector space

Note 1 to entry: An n-dimensional vector is represented by an ordered set of n scalars, usually real or complex numbers, which depend on the choice of the base. In matrix notation, these scalars are usually represented as a column matrix:
U=( U 1 U 2 U n ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwfacqGH9aqpda qadaqaauaabeqGeeaaaaqaaiaadwfadaWgaaqaaKqzGeGaaGymaaGc beaaaeaacaWGvbWaaSbaaeaajugibiaaikdaaOqabaaabaGaeSO7I0 eabaGaamyvamaaBaaabaGaamOBaaqabaaaaaGaayjkaiaawMcaaaaa @4546@

Note 2 to entry: A vector in a Euclidean space is characterized by its magnitude and, if it is a non-zero vector, by its direction.

Note 3 to entry: A complex vector U is defined by a real part and an imaginary part:
U=A+jB MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaKqzafGaaCyvaiabg2 da9iaahgeacqGHRaWkcaGGQbGaaCOqaaaa@3EC5@ where A and B are real vectors.

Note 4 to entry: A vector is indicated by a letter symbol in sloped boldface type or by an arrow above a sloped lightface letter symbol: U or U MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaa4WaaCbiaKqzafqaai aadwfaaeqaleaacWaGKAOKH4kaaaaa@3DC6@ . The vector U with components U i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadwfadaWgaaWcba qcLboacaWGPbaaleqaaaaa@3C1A@ can be denoted ( U i ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaKqzafGaaiikaiaadw fakmaaBaaaleaajug4aiaadMgaaSqabaGccaGGPaaaaa@3E36@ .

Note 5 to entry: The term "vector" is also used for a vector quantity.

Note 6 to entry: In geometry, the term “vector” is often used for a directed line segment in a point space.


Publication date:2017-07
Source:
Replaces:102-03-04:2007-08
Internal notes:
CO remarks:
TC/SC remarks:
VT remarks:
Domain1:
Domain2:
Domain3:
Domain4:
Domain5: