16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 3.5.12

Linear Transformations

Mathematics — Linear Algebra · extension-of-linear-functional

Problem

Let

V

be a finite-dimensional vector space over the field

F

and let

W

be a subspace of

V

. If

f

is a linear functional on

W

, prove that there is a linear functional

g

V

such that

g(\alpha) = f(\alpha)

for each

\alpha

in the subspace

W