vectorelement

A vectorelement, often called a component or coordinate, is an individual entry that makes up a vector. In mathematics, a vector is an ordered collection of scalars; each entry is a vector element. In computer science and data processing, a vector (or dynamic array) has elements stored in sequence, and each element is a vector element.

In linear algebra, a vector in a finite-dimensional space with basis {e1, ..., en} is written as v = v1 e1 + ... + vn en. The scalars vi are the vector elements (or coordinates) of v with respect to that basis, and the tuple (v1, ..., vn) is its coordinate representation. The number of vector elements equals the dimension of the space.

In programming and data processing, vector elements are accessed by indices and can be manipulated elementwise. Common operations include addition, scalar multiplication, and dot products, all of which act on corresponding vector elements.

Examples: In R^3, the vector v = (2, -5, 7) has three vector elements: 2, -5, and 7. With the standard basis, these are the coordinates along the x, y, and z directions.

Terminology varies: some authors prefer component or coordinate over vector element. The term emphasizes the role of the entry as part of a vector, though its exact meaning can depend on context, especially when comparing concrete coordinate representations to abstract vector spaces.