No Bullshit Guide to Linear Algebra

✍ Scribed by Ivan Savov

• Publisher: Minireference Co.
• Year: 2020
• Tongue: English
• Leaves: 599
• Edition: 2.2
• Category: Library

✦ Table of Contents

Preface
Introduction
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
Intro to linear algebra
Definitions
Vector operations
Matrix operations
Linearity
Overview of linear algebra
Introductory problems
Computational linear algebra
Reduced row echelon form
Matrix equations
Matrix multiplication
Determinants
Matrix inverse
Computational problems
Geometric aspects of linear algebra
Lines and planes
Projections
Coordinate projections
Vector spaces
Vector space techniques
Geometric problems
Linear transformations
Linear transformations
Finding matrix representations
Change of basis for matrices
Invertible matrix theorem
Linear transformations problems
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
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
Probability theory
Probability distributions
Markov chains
Google's PageRank algorithm
Probability problems
Quantum mechanics
Introduction
Polarizing lenses experiment
Dirac notation for vectors
Quantum information processing
Postulates of quantum mechanics
Polarizing lenses experiment revisited
Quantum mechanics is not that weird
Quantum mechanics applications
Quantum mechanics problems
End matter
Conclusion
Social stuff
Acknowledgements
General linear algebra links
Answers and solutions
Notation
Math notation
Set notation
Vectors notation
Complex numbers notation
Vector space notation
Abstract vector spaces notation
Notation for matrices and matrix operations
Notation for linear transformations
Matrix decompositions
Index