I am a beginner to real maths and am looking at a problem from a book by Loomis and Sternberg.
Let be the linear transformation from to such that .
I need to show that is an isomorphism if is a bijection by showing that:
(a) injective -> surjective;
(b) surjective -> injective.
I'm not really sure where to start, and I can't even see the link between the properties of the 2 mappings; any hints would be greatly appreciated.