Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares

Seconded. The full name of the book is; Practical Linear Algebra: A Geometry Toolbox. The preface states The subtitle of this book is A Geometry Toolbox; this is meant to emphasize that we approach linear algebra in a geometric and algorithmic way (The first edition was named "The Geometry Toolbox for Graphics and Modeling"). Pair it with Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares by Boyd and Vandenberghe (https://web.stanford.edu/~boyd/vmls/) and you are golden.

I work in that area :) The skills needed will vary a lot. Hence my concern about studying H&H. It's a good idea, as real analysis is the foundation. But it will take too much of your time to get to something useful. Probably you should try to learn more applied material in parallel and let both threads merge in the future. For maximum likelihood, you need to learn convex optimization right after real analysis. The canonical reference is [1], but there's also a very simple and pragmatic linear algebra textbook by the same author that also covers some of the optimization basics [2]. This might be a good entry point, certainly easier than Spivak or H&H. There's also [3,4], which you probably know about. These are great and emphasize the modeling part. Maximum likelihood (via EM) is in the appendix, and you don't really need to know a lot of math to get going.…

Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares : https://web.stanford.edu/~boyd/vmls/

Linear algebra, and more than one such book. IMHO long and still the best linear algebra book is Halmos, Finite Dimensional Vector Spaces (FDVS). It was written in 1942 when Halmos was an "assistant" to John von Neumann at the Institute for Advanced Study. It is intended to be finite dimensional vector spaces but done with the techniques of Hilbert space. The central result in the book, according to Halmos, is the spectral decomposition. One result at a time, the quality of von Neumann comes through. Commonly physicists have been given that book as their introduction to Hilbert space for quantum mechanics. But FDVS is a little too much for a first book on linear algebra, or maybe even a second book, should be maybe a third one. Also high quality is Nering, Linear Algebra and Matrix Theory. Again, the quality comes through: Nering was a student of Artin at Princeton. There Nering does most of linear algebra on just finite fields, not just the real and complex fields; finite fields in linear algebra are important in error correcting codes. So, that finite field work is a good introduction to abstract algebra.…