In this book, I avoided all but the most routine parts of this information. The book is a great introduction, but I think only at this book would one be able to master all the material summarized in the title.
Why is Linear Algebra taught in Quantum Physics or Engineering? I did not even know I had its answer until an extremely astute Physics professor told me. The proper answer is that in typical linear systems of equations or differential equations we are dealing with physical quantities that are linear operators, but the application of the same ideas to vastly different sets of problems leads to uncertainty and in a strictly quantum-thinking calculus is the source of Schr%C3%B6dinger's Cat .
Although, I do recommend this book, and the author @McPhersonLowe , I do recommend it because it is both rigorous and a great source for lots of applicable examples. The author does a great job of breaking linear algebra down to its most basic elements.
This is definitely not an introductory text, but it gives the basic ingredients of the material of many introductory texts, in an optional-for-the-junior course. There is very little work on matrices, but instead the reader is encouraged to focus on ring theory and non-commutative algebra, and finite-dimensional spaces, linear maps, etc. 7211a4ac4a