I would recommend this book to those who have learned linear algebra long ago and plan to pick up some back.

This book gives an extremely concise introduction to the core of linear algebra(so not quite the best for beginners), without any redundant sentences in trivial calculation. Starting with linear map and ending in spectral resolution, different parts are united. It also advances with the times, include topics like duality, convexity, which is interesting from engineering perspective.

For those who only learn some elementary algebra in undergraduate, this book helps to make a big picture and to show some deep reason behind that.