No Bullshit Guide to Linear Algebra

by Ivan Savov

Overview

Linear algebra is the foundation of science and engineering. Knowledge of linear algebra is a prerequisite for studying statistics, machine learning, computer graphics, signal processing, chemistry, economics, quantum mechanics, and countless other applications. Indeed, linear algebra offers a powerful toolbox for modelling the real world.

The No Bullshit Guide to Linear Algebra shows the connections between the computational techniques of linear algebra, their geometric interpretations, and the theoretical foundations. This university-level textbook contains lessons on linear algebra written in a style that is precise and concise. Each concept is illustrated through definitions, formulas, diagrams, explanations, and examples of real-world applications. Readers build their math superpowers by solving practice problems and learning to use the computer algebra system SymPy to speed up tedious matrix arithmetic tasks.

"The book explains the concepts in a way that gives a strong intuitive understanding." - Joe Nestor, student

"It's very well written and a fun read!" - Felix Kwok, professor

"I used this book in multiple big data courses when I needed a deeper understanding of the material." - Zane Zakraisek, student

The author, Ivan Savov, combines 17 years of tutoring experience with a B.Eng. in electrical engineering, an M.Sc. in physics, and a Ph.D. in computer science from McGill University.

Product Details

ISBN-13:	9780992001025
Publisher:	Minireference Co.
Publication date:	10/25/2020
Edition description:	2nd V2.2 ed.
Pages:	596
Product dimensions:	5.50(w) x 8.50(h) x 1.21(d)

About the Author

Ivan Savov combines 17 years of tutoring experience with a B.Eng. in electrical engineering, an M.Sc. in physics, and a Ph.D. in computer science from McGill University. Tutoring made him realize that understanding connections between concepts is much more important than memorizing facts. It's not about how many equations you know, but about knowing how to get from one equation to another. He founded the Minireference Publishing company to start a revolution in the textbook industry by making textbooks that don't suck.

Table of Contents

• Preface
• Introduction
• 1 Math fundamentals
• Solving equations
• Numbers
• Variables
• Functions and their inverses
• Basic rules of algebra
• Solving quadratic equations
• The Cartesian plane
• Functions
• Functions reference
• Geometry
• Trigonometry
• Trigonometric identities
• Vectors
• Complex numbers
• Solving systems of linear equations
• Set notation
• Math problems
• 2 Intro to linear algebra
• Definitions
• Vector operations
• Matrix operations
• Linearity
• Overview of linear algebra
• Introductory problems
• 3 Computational linear algebra
• Reduced row echelon form
• Matrix equations
• Matrix multiplication
• Determinants
• Matrix inverse
• Computational problems
• 4 Geometric aspects of linear algebra
• Lines and planes
• Projections
• Coordinate projections
• Vector spaces
• Vector space techniques
• Geometric problems
• 5 Linear transformations
• Linear transformations
• Finding matrix representations
• Change of basis for matrices
• Invertible matrix theorem
• Linear transformations problems
• 6 Theoretical linear algebra
• Eigenvalues and eigenvectors
• Special types of matrices
• Abstract vector spaces
• Abstract inner product spaces
• Gram--Schmidt orthogonalization
• Matrix decompositions
• Linear algebra with complex numbers
• Theory problems
• 7 Applications
• Balancing chemical equations
• Input--output models in economics
• Electric circuits
• Graphs
• Fibonacci sequence
• Linear programming
• Least squares approximate solutions
• Computer graphics
• Cryptography
• Error-correcting codes
• Fourier analysis
• Applications problems
• 8 Probability theory
• Probability distributions
• Markov chains
• Google's PageRank algorithm
• Probability problems
• 9 Quantum mechanics
• Introduction
• Polarizing lenses experiment
• Dirac notation for vectors
• Quantum information processing
• Postulates of quantum mechanics
• Quantum mechanics is not that weird
• QM applications
• QM problems
• End matter
• A Answers and solutions
• B Notation
• Index

Editorial Reviews

Very accessible review of the topic and a pleasure to read. I wish I had this as a guide university as it is much clearer than my professors or those much more expensive official textbooks. This book, along with Math & Physics are proving very useful as I review the topics for some exploration at work. -- Rod

I spent my whole life hating mathematics until I started reading that book. Now all I wanna do in my free time is to solve math problems. That's how good this book is. I wish Ivan Savov would write a book like that for every math subject. -- Charles

Very well written, I recommend the book to university students as complementary reading. -- Hynek

This guy does the job in conveying concepts, which can at times be abstract. The ideas/definitions are theoretically the same as most texts, but the structure of the chapters, writing style, and explanations are much more effective. I have read multiple college texts and \"knew\" the definitions but didn't really understand the \"picture\" of many definitions from basic determinant and dot product to coordinate matrix relative to a basis. This text made me feel I know what they are and why they are used that way.

This is one of the most useful math education books I have read. It's intro math review is excellent in itself. For me the book has a perfect pace, it is succinct without being overwhelming and clips along and an enjoyable pace. There are plenty of useful exercises. There is also some humour embedded into some of the test questions. The book has helped me beef up my linear algebra study for following Andrew Ng's courses.

Linear algebra now makes sense and has been given meaning to me it never had before.

I'm an experienced statistician with math background. I leaned linear algebra in both undergraduate math and graduate stats courses the old fashion way-dry and boring. I really didn't get the concept and geometric interpretation until later. I wish I had gotten sooner, in the class room, with book like this one. It'd make learning much more fun and 'get the point' of this subject. I enjoy reading this book and doing the exercises. For those who aspire to do data analysis for a living, I highly recommend this book. It's not enough to know high-level, reader's digest versions of data-mining algorithms. Without understanding the math behind sexy algorithms, it's easy to mis-use them and don't realize it. I've seen plenty instances of that.

See dozens more reviews here: https: //www.amazon.com/product-reviews/0992001021/

From the Publisher