IEVref: 102-03-08 ID: Language: en Status: Standard Term: base, Synonym1: basis [Preferred] Synonym2: Synonym3: Symbol: Definition: ordered set of n linearly independent vectors ${a}_{1}\text{,}\text{\hspace{0.17em}}{a}_{2}\text{,}\text{\hspace{0.17em}}...\text{,}\text{\hspace{0.17em}}{a}_{n}$ in an n-dimensional vector space, which is chosen to express any vector U as a unique linear combination of these n vectors$U={U}_{1}{a}_{1}+{U}_{2}{a}_{2}+...+{U}_{n}{a}_{n}$, where ${U}_{1}\text{,}\text{\hspace{0.17em}}{U}_{2}\text{,}\text{\hspace{0.17em}}...\text{,}\text{\hspace{0.17em}}{U}_{n}$ 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". 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: