Practical linear algebra
by Gerald E. Farin · first published 2013
100% recommend
Why HN recommends it
Visual, geometry-first introduction to linear algebra that builds intuition beyond mechanical computation; suits beginners and visual learners, and pairs well with coordinate geometry and trigonometry.
Summarised by Claude from recommending comments
"Practical Linear Algebra covers all the concepts in a traditional undergraduate-level linear algebra course, but with a focus on practical applications. The book develops these fundamental concepts in 2D and 3D with a strong emphasis on geometric understanding before presenting the general (n-dimensional) concept. The book does not employ a theorem/proof structure, and it spends very little time on tedious, by-hand calculations (e.g., reduction to row-echelon form), which in most job applications are performed by products such as Mathematica. Instead the book presents concepts through example
Affiliate links. As an Amazon Associate I earn from qualifying purchases.
Mentions per year
What Hacker News says
Related books
2020–2026Introduction to Applied Linear Algebra
Stephen Boyd, Lieven Vandenberghe
Recommended by 7 · mentioned by 107 recommend · 10 mention7 recommend · 107 recommend
2008–2026Linear Algebra Done Right
Sheldon Jay Axler
Recommended by 130 · mentioned by 179130 recommend · 179 mention130 recommend · 179130 recommend
2013–2026No bullshit guide to linear algebra
Ivan Savov
Recommended by 15 · mentioned by 1915 recommend · 19 mention15 recommend · 1915 recommend
2013–2026Coding the Matrix
Philip N. Klein
Recommended by 31 · mentioned by 4131 recommend · 41 mention31 recommend · 4131 recommend
Maybe this book will also be of interest: http://www.amazon.com/Practical-Linear-Algebra-Geometry-Tool...
on “A Geometric Review of Linear Algebra [pdf]” ↗belfalas you probably feel you don't need another one but this is a great book that is friendly for visual learners (even though apparently they don't exist!) Practical Linear Algebra - Gerald Farin & Dianne Hansford. IIRC, the first edition was based on a work designed to educate design workers at a car firm who either didn't have the background or needed shoring up. So from the…
on “Ask HN: Best beginner friendly linear algebra book?” ↗You need this book: Practical Linear Algebra: A Geometry Toolbox by Gerald Farin and Dianne Hansford. You can get older editions for pennies. The 1st edition was actually called The Geometry Toolbox for Graphics and Modeling. You should also read…
on ““When are we going to use this in our everyday life?” (2017)” ↗…interpretation simultaneously in mind. The basic example of solving a system of linear equations in two variables will cement this idea when you map it to the XY coordinate system. You might find the book Practical Linear Algebra : A Geometry Toolbox by Farin and Hansford useful for further study.
on “Linear Algebra for Programmers” ↗…edition available). 2) Mathematical Principles for Scientific Computing and Visualization by Gerald Farin and Dianne Hansford - Nice overview of needed background. The authors also have a book named Practical Linear Algebra: A Geometry Toolbox which you might find a ideal companion. 3) Numerical Methods: Fundamentals and Applications by Rajesh Kumar Gupta - A relatively recent book with a really broad coverage of subjects…
on “Ask HN: What to learn for math for modeling?” ↗…wrong message from these comments. Mathematicians/Practitioners know when to switch from simple geometry to algebra and that is taught as a matter of course. As an example, the farin and hansford book Practical Linear Algebra: A Geometry Toolbox that i mention at https://news.ycombinator.com/item?id=45060305 precisely takes this approach starting with visualizing vectors in 2D/3D geometry and then moving on to higher-dimensions.…
on “Ask HN: What to learn for math for modeling?” ↗You might want to checkout the book Practical Linear Algebra: A Geometry Toolbox by Dianne Hansford and Gerald Farin (its 1st edition was simply named The Geometry Toolbox: For Graphics and Modeling) to get an intuitive and visual introduction to Linear Algebra.…
on “The Little Book of Linear Algebra” ↗…thinkers who might be looking for a linear algebra book that focuses more on developing the geometric intuition for stuff like this, rather than just pure numeric linear system solving, let me recommend: "Practical Linear Algebra: A Geometry Toolbox" by Farin and Hansford.
on “Matrices can be your friends (2002)” ↗…obscured by the pedantic formalism espoused by the teaching community. Linear Algebra SHOULD always be taught alongside Coordinate/Analytic Geometry and Trigonometry for proper intuition. I found the book "Practical Linear Algebra: A Geometry Toolbox" very helpful in my study.
on “Relearning Matrices as Linear Functions” ↗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…
on “Ask HN: Best beginner friendly linear algebra book?” ↗…mechanical operations that computers do better. There are better approaches! Linear Algebra Done Right (S. Axler), for example, is one of the few books that justifies the definition of matrix multiplication. Practical Linear Algebra does everything visually, and is suitable for beginners. But the first text is only taught to math majors, and the second one is not widely used. In any case, I am highly opposed to teaching the mechanics…
on “Matrix Multiplication” ↗…in 3 dimensions works for N dimensions. You can build up a very working, visual intuition for Linear Algebra just by doing everything in 3D, for example. There's a textbook that takes this approach: "Practical Linear Algebra". But, of course, this comes with a caveat: it works until it doesn't. The volume of a unit sphere increases for dimensions 1-5, then starts to go down[1]. There exists an exotic R^4: a manifold that…
on “Mathematics as thought” ↗