basistype

Basistype is a term used in mathematics and computer science to describe the kind of basis used to represent elements of a vector space, function space, or data space. It is not a single object but a classification of the representation method chosen for a particular problem.

In linear algebra, a basis is a set of vectors that are linearly independent and span the space. A basistype specifies properties of that basis and can influence computational behavior. Common basistypes include the canonical (standard) basis, where each basis vector has a single nonzero entry; an orthonormal basis, where vectors are mutually orthogonal and of unit length; and an orthogonal basis, where vectors are mutually orthogonal but may have arbitrary length. For function spaces, basistypes include Fourier or cosine bases, polynomial bases such as monomials or Legendre polynomials, and wavelet or spline bases.

The choice of basistype affects representations and operations. A vector is expressed as coordinates relative to the chosen basis, and changing the basistype requires a change-of-basis transformation, typically via a basis matrix. Sparsity, numerical stability, and efficiency are often reasons to prefer one basistype over another in a given application.

In software and data science, basistype can also function as metadata describing how data is organized or how linear-algebra routines should be applied, enabling specialized implementations for performance or accuracy.

See also: Basis, Change of basis, Vector space, Coordinate system.