Let be a linear map between vector spaces. Show that T is injective if and only if .
Proof:
Suppose first that T is injective. Then implies , so .
Now suppose . Then implies which implies , and . So, T is injective.
Filed under: Algebra, Linear Algebra, Proof of the Day | Tagged: injective, kernel, linear transformation, map, one to one, space, vector | Leave a Comment »
