Definition – Linear Functional

Contents

  1. Definition
  2. Theorems.
    i)
  3. Related definitions.

Definition

Let V be a vector space over a field F . Let f be a function f: V \rightarrow F such that for all a, b \in F and \mathbf{x,y} \in V,

f(a\mathbf{x} + b\mathbf{y}) = af(\mathbf{x}) + bf(\mathbf{y}).

If f is such a function as defined above, then f is a linear functional on V .