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IEVref: | 102-03-08 | ID: | |

Language: | en | Status: Standard | |

Term: | base, <in linear algebra> | ||

Synonym1: | basis [Preferred] | ||

Synonym2: | |||

Synonym3: | |||

Symbol: | |||

Definition: | ordered set of n linearly independent vectors ${a}_{1}\text{,}\text{\hspace{0.17em}}{a}_{2}\text{,}\text{\hspace{0.17em}}\mathrm{...}\text{,}\text{\hspace{0.17em}}{a}_{n}$ in an n-dimensional vector space, which is chosen to express any vector as a unique linear combination of these Un vectors$U={U}_{1}{a}_{1}+{U}_{2}{a}_{2}+\mathrm{...}+{U}_{n}{a}_{n}$, where ${U}_{1}\text{,}\text{\hspace{0.17em}}{U}_{2}\text{,}\text{\hspace{0.17em}}\mathrm{...}\text{,}\text{\hspace{0.17em}}{U}_{n}$ are scalars Note 1 to entry: In an Euclidean or Hermitian vector space, an orthonormal base is generally chosen. In the vector space formed by a set of Note 2 to entry: Any vector of a base is called "base vector". | ||

Publication date: | 2017-07 | ||

Source: | |||

Replaces: | 102-03-08:2007-08 | ||

Internal notes: | |||

CO remarks: | |||

TC/SC remarks: | |||

VT remarks: | |||

Domain1: | |||

Domain2: | |||

Domain3: | |||

Domain4: | |||

Domain5: |

$U={U}_{1}{a}_{1}+{U}_{2}{a}_{2}+\mathrm{...}+{U}_{n}{a}_{n}$, where ${U}_{1}\text{,}\text{\hspace{0.17em}}{U}_{2}\text{,}\text{\hspace{0.17em}}\mathrm{...}\text{,}\text{\hspace{0.17em}}{U}_{n}$ are scalars

Note 1 to entry: In an Euclidean or Hermitian vector space, an orthonormal base is generally chosen. In the vector space formed by a set of *n-*bit words (see Note 1 to entry in IEV 102-03-01, vector space) a base is the set of *n-*bit words having only one non-zero bit.

Note 2 to entry: Any vector of a base is called "base vector".