Definition:Dual Vector Space

This page is about Dual Vector Space in the context of Linear Algebra. For other uses, see Dual.

Definition

Let $V$ be a vector space.

Let $\phi: V \to \R$ be a linear mapping.

The set of all $\phi$ is called a dual space (of $V$) and is denoted by $V^*$.

Also see

• Definition:Algebraic Dual: the concept as applied to a module over a general commutative ring
• Definition:Normed Dual Space

Sources

• 1964: Peter Freyd: Abelian Categories ... (previous) ... (next): Introduction
• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.): Appendix $\text B$. Review of Tensors