Interface VectorSpace<V,F>

All Superinterfaces:
AbelianGroup<V>, AbelianMonoid<V>, Group<V>, Magma<V>, Module<V,F>, Monoid<V>, Set<V>
All Known Implementing Classes:
VectorSpace2D, VectorSpace3D
public interface VectorSpace<V,F> extends Module<V,F>
A vector space is a module over a field.

This is the central structure of linear algebra.

Mathematical Definition

A vector space V over a field F is a module where the scalar ring is a field. Elements of V are called vectors, elements of F are called scalars.

Examples

  • ℝⁿ (Euclidean space)
  • ℂⁿ (Complex coordinate space)
  • Function spaces (e.g., L²)
  • Polynomial spaces
Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Method Details

    • getScalarField

      default Field<F> getScalarField()
      Returns the field of scalars.
      Returns:
      the scalar field

    • dimension

      default int dimension()
      Returns the dimension of the vector space (if finite).
      Returns:
      the dimension, or -1 if infinite/unknown