Linear Algebra: Step by Step 1st Edition

This is my third Linear Algebra textbook that I am using to learn the math on my own. I left off from mathematics with Calculus 3 about 15 years ago and wanted to learn what Eigen functions and values were about.This textbook is very methodical and thorough. The author has taken the advice of many of his students and those from other countries to craft a book that will make the math clear. I would say that this book is for the mathematically challenged like myself. That is not to say it is simplistic, one must have a firm grasp of algebra and calculus to get through it.Compared to the other two books, this one is more practical than theoretical. This is what I want in a book because I am learning linear algebra to understand quantum physics; I am not interested in being a theoretical mathematician. One of the previous books I have tried is heavy on mathematical logic which makes no sense to me. This book does not try to frame theorems or problems in mathematical logic.The solutions to the problems at the end of each section are detailed on the author's web site. These are done thoroughly so the student can see each step.The author gives instruction on how to use MATLAB for linear algebra. I have down loaded MATLAB but so far have not found an instruction manual as to how to use it.The author takes time to go over the historical persons who have contributed to linear algebra such as Gauss, Cayley and others which I find interesting and important.The only fault with the book is the small font in the examples. The print is readable but it it causes eye strain after a while.This is a book with the student of average mathematical ability in mind, not for the MIT or Caltech genius.

I purchased this book to study linear algebra “step by step” as it says on the title. And this book is not lying; it actually teaches you linear algebra step by step.One of the great things about this book is that it reviews (and expands) previous concepts whenever it moves on from matrix algebra to general vector spaces. This really makes the book self contained, and suitable for self study. Not to mention, all of the answers to the exercises are posted online (even the proof questions!) by the author, and (although I did not use it) the lectures are also posted online.The proofs in this book can sometimes be dry, but it is very clear on communicating how the proof goes. There are mostly no gaps to fill in the proofs, and also has “what does this mean?” section where it explains less formally what the proposition or theorem is saying.Overall a very beginner friendly book, but also a perfect reference when you don’t understand other book’s proof styles. I moved on to Linear Algebra Done Right (LADR) starting from general vector spaces, but this book is still very helpful when LADR isn’t clear enough.If you want a perfect book for self study, or just a reference for clear proofs, this is the book for you.

"LINEAR ALGEBRA" by Kuldeep Singh is a great book!As a retired high school physics teacher I have enjoyed working thru quite a few text books dealing with Math, Physics, Astronomy, and Astrophysics. This book is one of the best! Its a perfect book for doing a self-study of Linear Algebra!In my opinion there are 2 things that make "Linear Algebra" by Kuldeep Singh great for self-study:#1. The book's conversational style. Instead of ideas being presented in a matter-of-fact way, the author gives you the feeling he is actually talking to you. For example, the text abounds with comments and questions which the author anticipates the reader might make or ask following important ideas: "Remember...", "Why is that?", "What does this mean?", "Can you think of why?", "How do we do this?", "You might like to show...", "This might be a bit hard to grasp on first reading...". He then explains clearly, often with examples, the answers to the questions as the ideas are presented.#2. The author provides ALL the answers and complete solutions to the problems at the end of each section and chapter. This is incredibly important for someone like me doing a self-study to confirm that I am understanding the material.Chapter topics include:#1 LINEAR EQUATIONS AND MATRICES: Systems, Gaussian Elimination, Matrix Algebra, Transpose and Inverse, Types of Solutions#2 EUCLIDEAN SPACES: Vector Properties, Basis, Spanning Sets, Linear Independence#3 GENERAL VECTOR SPACES: Linear Independence and Basis, Subspaces, Dimensions, Linear Systems#4 INNER PRODUCT SPACES: Inequalities, Orthogonality and Orthogonal Matrices, Orthonormal Basis#5 LINEAR TRANSFORMATIONS: Kernal, Range, Rank, Nullity, Matrices in Linear Transformations#6 DETERMINANTS AND THE INVERSE MATRIX: Properties, LU Factorization#7 EIGENVALUES AND EIGENVECTORS: Properties, Diagonalization, Symmetric Matrices, Singular Value Decomposition.The book is loaded with detailed examples which clearly show the concepts being discussed. Each chapter also contains short historical biographies in which key people in the development of the field of Linear Algebra are presented and each chapter ends with an interview of someone currently in the field showing how linear algebra is important for what they do.