Kunze Linear Algebra · Problem 3.6.2

Linear Transformations

Mathematics — Methods · subspace-intersection-null-spaces

Problem

Use Theorem 20 to prove the following. If

W

is a subspace of a finite-dimensional vector space

V

and if

\{g_1, \ldots, g_r\}

is any basis for

W^0

, then

W = \bigcap_{i=1}^{r} N_{g_i}.