$U=U_1{a}_1+U_2{a}_2+\mathrm{...}+U_n{a}_n$, where $U_1\text{,}{U}_2\text{,}\mathrm{...}\text{,}{U}_n$ 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".