No Bullshit Guide to Linear Algebra

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