No Bullshit Guide to Linear Algebra

Description

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