Linear Algebra with Applications by Bretscher

[micromass]

• Author: Otto Bretscher
• Title: Linear Algebra with Applications
• Amazon Link: https://www.amazon.com/dp/0136009263/?tag=pfamazon01-20

Table of Contents:

[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]

 

[dkotschessaa]

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