Linear Algebra for Physicists and Engineers: Volume 1

Often when a math book is “for physicists and engineers,” that means that it is less serious and ambitious than math books for mathematicians. Usually it means it is kind of watered down. But this could stand as a really good book for mathematicians too. In most senses, it's more ambitious than most beginning books on linear algebra. But the book works its way gently up to each pinnacle. The only sense in which it's watered down is that there aren't a lot of difficult proofs. But deep ideas are treated in depth.The book is great in a lot of places. But I especially like this treatments of determinants, orthogonal matrices, the Caley-Hamilton theorem, and tensor products. There is a lot that I was confused about that I understand now.