Linear Algebra

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Table of Contents some of the Open Books

Interactive Linear Algebras by Dan Margalit

  1. Systems of Linear Equations: Algebra (pp 1-27)

  2. Systems of Linear Equations: Geometry (pp 29-112)

  3. Linear Transformations and Matrix Algebra (pp 113-185)

  4. Determinants (pp 187-235)

  5. Eigenvalues and Eigenvectors (pp 237-337)

  6. Orthogonality (pp 339-407)

Discover Linear Algebra by Jeremy Sylvestre

  1. Systems of Equations and Matrices (pp 7-169)

    • Systems of linear equations

    • Solving systems using matrices

    • Using systems of equations

    • Matrices and matrix operations

    • Matrix inverses

    • Elementary matrices

    • Special forms of square matrices

    • Determinants

    • Determinants versus row operations

    • Determinants, the adjoint, and inverses

  2. Vector Spaces (pp 170-374)

    • Introduction to vectors

    • Geometry of vectors

    • Orthogonal vectors

    • Geometry of linear systems

    • Abstract vector spaces

    • Subspaces

    • Linear independence

    • Basis and Coordinates

    • Dimension

    • Column, row, and null spaces

  3. Introduction to Matrix Forms (pp 375-413)

    • Eigenvalues and eigenvectors

    • Diagonalization

Linear Algebra by Jim Hefferon

  1. Linear Systems

    • Solving Linear Systems

    • Linear Geometry

    • Reduced Echelon Form

  2. Vector Spaces

    • Definition of Vector Space

    • Linear Independence

    • Basis and Dimension

  3. Maps Between Spaces

    • Isomorphisms

    • Homomorphisms

    • Computing Linear Maps

    • Matrix Operations

    • Change of Basis

    • Projection

  4. Determinants

    • Definition

    • Geometry of Determinants

    • Laplace's Formula

  5. Similarity

    • Complex Vector Spaces

    • Similarity

    • Nilpotence

    • Jordan Form

A First Course in Linear Algebra by Robert A. Beezer

  1. Systems of Linear Equations

  2. Vectors

  3. Matrices

  4. Vector Spaces

  5. Determinants

  6. Eigenvalues

  7. Linear Transformations

  8. Representations

Linear Algebra, Theory And Applications by Kenneth Kuttler

  1. Preliminaries

  2. Matrices and Linear Transformations

  3. Determinants

  4. Row Operations

  5. Some Factorizations

  6. Linear Programming

  7. Spectral Theory

  8. Vector Spaces and Fields

  9. Linear Transformations

  10. Linear Transformations Canonical Forms

  11. Markov Chains and Migration Processes

  12. Inner Product Spaces

  13. Self Adjoint Operators

  14. Norms for Finite Dimensional Vector Spaces

  15. Numerical Methods for Finding Eigenvalues

MATH 1220 Linear Algebra 1 by Michael Doob

  1. Systems of Linear Equations

  2. Matrix theory

  3. The Determinant

  4. Vectors in Euclidean n-space

  5. Eigenvalues and eigenvectors

  6. Linear transformations

Markov Chains

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