Linear Algebra Demystified

David McMahon

July 2006 · McGraw Hill Professional

About this eBook

Taught at junior level math courses at every university, Linear Algebra is essential for students in almost every technical and analytic discipline.

Ratings and reviews

Dont use this book alone. Without a good foundation on the math used, you will be confused by it's errors. At one place it confuses the different notations for christoffel symbols and that makes it hard to undenderstand some of the future dirivations.

  I love this book and I hate it, and here's why. This is a terrific book to quiz yourself with and test your knowledge, but this book alone will NOT teach you, explain things, or "de-mystify" anything. It certainly doesn't live up to its title. Sadly, it's still better than most textbooks. I suggest 2books: One linear algebra book (that isn't this) to teach you, and afterwards use this book to quiz yourself. There aren't enough graphs, etc, to visualize the things we are dealing with. When inverting a 3x3 matrix you 1st obtain the matrix of minors. Instead of shading a cross over the row and column position of the desired element, he lists them!! How is anyone going to see a connection between the determinate of "sub-matrix" [a22, a23, a32, a33] and the next "sub-matrix" determinate? There is often little or no information explaining the symbols and notation we use. That's actually one of my biggest problems. Every vector should have an arrow, and we should talk about it, lets talk about unit vectors depicted with a hat, let's talk about [3,-2,4] and <3,-2,4> and (3,-2,4) and {3,-2,4} let's talk about |u| and ||u|| because these subtleties matter. Sometimes things are described in words and then you get to the quiz and there are symbols you've never seen before. Sometimes a Greek letter is introduced like lambda, or μ, and there is no indication if it's a variable, a function, a constant, a vector, or what the f*** and Greek is my 1st language. (Not that it matters in Math.) He does this on page 79. He shows you a vector: u=(3,-2,4) where μ is a vector in R^3. It's the 1st and last time you EVER hear a reference to μ in this book. Why? Why μ? Is it a typo? Is it supposed to be u? They're 2different fonts styles, 2 different languages, how does that happen? He only dedicates 5 sentences and 2 examples to explain the entire concept of n-tuples and vectors in R^n. Just once I'd like to see it written somewhere: R^2 is a 2-tuple, R^3 is a 3-tuple, C^n is an n-tuple, C^2 is a 2-tuple...do you know how much googling that would have saved me? The characteristic polynomial of an eigenvalue is full of unknowns. A massive equation starting with delta and riddled with S, without telling us what delta or S stands for. "Δ(λ)=λ^n-S1λ^(n-1)+S2λ^(n-2)+....+(-1)^n Sn" Thats no way to learn. Trust me, I know how to calculate |A-λI| by hand, and why not use sigma notation like: "Δ(λ)= ∑etc." if he wants to sum that kind of a sequence. Here's something else I found disturbing. It's a direct quote from page 76, chapter 4, paragraph 1, sentence 1: Chapter 4 Vectors "The reader is probably familiar with vectors from their use in physics and engineering. A vector is..." He actually started a chapter that way!!! This is supposed to be a Math book. Assume the reader knows Algebra 1, Geometry, Trigonometry, or whatever math courses generally precede Linear Algebra; don't assume the reader has any familarity with physics or engineering. So why do I keep checking these books out of the library if they make me so miserable and are confusing? 1) Its free. 2) As I mentioned, its still better than many other books on the subject. 3) The Quizzes! I know that if I can answer every question in a book this confusing, this vague, I will do great when asked something specific!

About the author

David McMahon works as a researcher at a National Laboratory, a Department of Energy facility. His research involves work on nuclear fusion and the design of nuclear-powered spacecraft. He has a master's degree in physics and a bachelor's in applied mathematics, both from the University of New Mexico at Albuquerque. He is currently doing research for a doctorate in theoretical physics in the areas of quantum field theory and the use of general relativity. Mr. McMahon is a published author. Previous work includes two books on computer programming: Rapid Application Development with Visual Basic 6 and Rapid Application Development with Visual C ++. He also wrote Quantum Mechanics Demystified, Relativity Demystified, and was a contributing writer to Ace the Technical Interview.