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Interactive Linear Algebra

Dan Margalit, Joseph Rabinoff

Front Matter

  * Colophon
  * Contributors to this textbook
  * Variants of this textbook
  * Overview

1Systems of Linear Equations: Algebra

  * Systems of Linear Equations
  * Row Reduction
  * Parametric Form

2Systems of Linear Equations: Geometry

  * Vectors
  * Vector Equations and Spans
  * Matrix Equations
  * Solution Sets
  * Linear Independence
  * Subspaces
  * Basis and Dimension
  * Bases as Coord 242 inate Systems
  * The Rank Theorem

3Linear Transformations and Matrix Algebra

  * Matrix Transformations
  * One-to-one and Onto Transformations
  * Linear Transformations
  * Matrix Multiplication
  * Matrix Inverses
  * The Invertible Matrix Theorem

4Determinants

  * Determinants: Definition
  * Cofactor Expansions
  * Determinants and Volumes

5Eigenvalues and Eigenvectors

  * Eigenvalues and Eigenvectors
  * The Characteristic Polynomial
  * Similarity
  * Diagonalization
  * Complex Eigenvalues
  * Stochastic Matrices

6Orthogonality

  * Dot Products and Orthogonality
  * Orthogonal Complements
  * Orthogonal Projection
  * Orthogonal Sets
  * The Method of Least Squares

Back Matter

  * Complex Numbers
  * Notation
  * Hints and Solutions to Selected Exercises
  * GNU Free Documentation License
  * Index
  * Colophon

 Index
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Interactive Linear Algebra


Dan Margalit
School of Mathematics
Georgia Institute of Technology

Joseph Rabinoff
School of Mathematics
Georgia Institute of Technology



June 3, 2019

ColophonContributors to this textbookVariants of this textbook
Overview
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