Math 060 101317 Linear Transformations: Isomorphisms

Lemma: Linear transformations that agree on a basis are identical. Definition: one-to-one (injective). Examples and non-examples. Lemma: T is one-to-one iff its kernel is {0}. Definition: onto (surjective). Examples and non-examples. Definition: isomorphism; isomorphic. Theorem: T is an isomorphism iff T is invertible. Exercise.