EWU Math 231: Linear Transformations - Bijective (Invertible) Linear Transformations

We discuss an invertible linear transformation and see that a linear transformation is invertible if and only if it is injective and surjective. Such transformations create a bridge between two (seemingly) different vector spaces in the sense that an invertible transformation T with domain U and codomain V establishes an isomorphism between U and V. In this case, we call U and V isomorphic. Of course, a composition of invertible linear transformations itself is invertible, and the inverse transformation is the composition of the inverse transformations in reverse order.