A vector is an ordered finite list of numbers. Its entries are called elements of the vector. The dimension of the vector is the number of elements it contains.
Denoting an \(n\)-dimensional vector using the symbol \(\pmb{a}\), the \(i\)-th element of the vector \(\pmb{a}\) is denoted with \(a_i\), where the subscript \(i\) is an integer index that runs from 1 to \(n\).
A vector is said to be sparse if many of its elements are zero, i.e. if \(a_i=0\) for many \(i\).