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Linear Algebra Linear Algebra with Applications by Bretscher

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  1. Jan 30, 2013 #1

    micromass

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    Table of Contents:
    Code (Text):

    [LIST]
    [*] Text Features
    [*] Preface
    [*] Linear Equations
    [LIST]
    [*] Introduction to Linear Systems
    [*] Matrices, Vectors, and Gauss-Jordan Elimination
    [*] On the Solutions of Linear Systems; Matrix Algebra
    [/LIST]
    [*] Linear Transformations
    [LIST]
    [*] Introduction to Linear Transformations and Their Inverses
    [*] Linear Transformations in Geometry
    [*] Matrix Products
    [*] The Inverse of a Linear Transformation
    [/LIST]
    [*] Subspaces of Mn and Their Dimensions
    [LIST]
    [*] Image and Kernel of a Linear Transformation
    [*] Subspaces of R^n; Bases and Linear Independence
    [*] The Dimension of a Subspace of R^n
    [*] Coordinates
    [/LIST]
    [*] Linear Spaces
    [LIST]
    [*] Introduction to Linear Spaces
    [*] Linear Transformations and Isomorphisms
    [*] The Matrix of a Linear Transformation
    [/LIST]
    [*] Orthogonality and Least Squares
    [LIST]
    [*] Orthogonal Projections and Orthonormal Bases
    [*] Gram-Schmidt Process and QR Factorization
    [*] Orthogonal Transformations and Orthogonal Matrices
    [*] Least Squares and Data Fitting
    [*] Inner Product Spaces
    [/LIST]
    [*] Determinants
    [LIST]
    [*] Introduction to Determinants
    [*] Properties of the Determinant
    [*] Geometrical Interpretations of the Determinant; Cramer’s Rule
    [/LIST]
    [*] Eigenvalues and Eigenvectors
    [LIST]
    [*] Dynamical Systems and Eigenvectors: An Introductory Example
    [*] Finding the Eigenvalues of a Matrix
    [*] Finding the Eigenvectors of a Matrix
    [*] Diagonalization
    [*] Complex Eigenvalues
    [*] Stability
    [/LIST]
    [*] Symmetric Matrices and Quadratic Forms
    [LIST]
    [*] Symmetric Matrices
    [*] Quadratic Forms
    [*] Singular Values
    [/LIST]
    [*] Linear Differential Equations
    [LIST]
    [*] An Introduction to Continuous Dynamical Systems
    [*] The Complex Case: Euler’s Formula
    [*] Linear Differential Operators and Linear Differential Equations
    [/LIST]
    [*] Appendix: Vectors
    [*] Answers to Odd-Numbered Exercises
    [*] Subject Index
    [*] Name Index
    [/LIST]
     
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jan 31, 2013 #2
    Using this book in my linear algebra course right now and I love the writing style, very clear examples and approach. There's even very cool historical examples, and splashes of wit/humor, but tastefully done.

    It's been criticized by some for some of it's notation, which people seem not to like or find weird, but which I actually find cool, but I'm a fan of inventive visual notation.

    -Dave K
     
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