Linear Algebra: A Modern Introduction by David Poole

[Greg Bernhardt]

• Author: David Poole
• Title: Linear Algebra: A Modern Introduction
• Amazon Link: https://www.amazon.com/dp/0538735457/?tag=pfamazon01-20
• Prerequisities:

Table of Contents:

[LIST]
[*] Vectors
[LIST]
[*] Introduction: The Racetrack Game
[*] The Geometry and Algebra of Vectors
[*] Length and Angle: The Dot Product
[*] Lines and Planes
[*] Code Vectors and Modular Arithmetic
[/LIST]
[*] Systems of Linear Equations
[LIST]
[*] Introduction: Triviality
[*] Introduction to Systems of Linear Equations
[*] Direct Methods for Solving Linear Systems
[*] Spanning Sets and Linear Independence
[*] Applications
[LIST]
[*] Allocation of Resources
[*] Balancing Chemical Equations
[*] Network Analysis
[*] Electrical Networks
[*] Finite Linear Games
[/LIST]
[*] Iterative Methods for Solving Linear Systems
[/LIST]
[*] Matrices
[LIST]
[*] Introduction: Matrices in Action
[*] Matrix Operations
[*] Matrix Algebra
[*] The Inverse of a Matrix
[*] The LU Factorization
[*] Subspaces, Basis, Dimension, and Rank
[*] Introduction to Linear Transformations
[*] Applications
[LIST]
[*] Markov Chains
[*] Population Growth
[*] Graphs and Digraphs
[*] Error-Correcting Codes
[/LIST]
[/LIST]
[*] Eigenvalues and Eigenvectors
[LIST]
[*] Introduction: A Dynamical System on Graphs
[*] Introduction to Eigenvalues and Eigenvectors
[*] Determinants
[*] Eigenvalues and Eigenvectors of [itex]n\times n[/itex] Matrices
[*] Similarity and Diagonalization
[*] Iterative Methods for Computing Eigenvalues
[*] Applications and the Perron-Frobenius Theorem
[LIST]
[*] Markov Chains
[*] Population Growth
[*] The Perron-Frobenius Theorem
[*] Linear Recurrence Relations
[*] Systems of Linear Differential Equations
[*] Discrete Linear Dynamical Systems
[/LIST]
[/LIST]
[*] Orthogonality
[LIST]
[*] Introduction: Shadows on a Wall
[*] Orthogonality in [itex]\mathbb{R}^n[/itex]
[*] Orthogonal Complements and Orthogonal Projections
[*] The Gram-Schmidt Process and the QR Factorization
[*] Orthogonal Diagonalization of Symmetric Matrices
[*] Applications
[LIST]
[*] Dual Cods
[*] Quadratic Forms
[*] Graphic Quadratic Equations
[/LIST]
[/LIST]
[*] Vector Spaces
[LIST]
[*] Introduction: Fibonacci in (Vector) Space
[*] Vector Spaces and Subspaces
[*] Linear Independence, Basis and Dimension
[*] Change of Basis
[*] Linear Transformations
[*] The Kernel and Range of a Linear Transformation
[*] The Matrix of a Linear Transformation
[*] Applications
[LIST]
[*] Homogeneous Linear Differential Equations
[*] Linear Codes
[/LIST]
[/LIST]
[*] Distance and Approximation
[LIST]
[*] Introduction: Taxicab Geometry
[*] Inner Product Spaces
[*] Norms and Distance Functions
[*] Least Square Approximation
[*] The Singular Value Decomposition
[*] Applications
[LIST]
[*] Approximation of Functions
[*] Error-Correcting Codes
[/LIST]
[/LIST]
[*] Appendix: Mathematical Notation and Methods of Proof
[*] Appendix: Mathematical Induction
[*] Appendix: Complex Numbers
[*] Appendix: Polynomials
[*] Answers to Selected Odd-Numbered Exercises
[*] Index
[/LIST]

 

[halo31]

It's a very nice textbook. Offers a good introduction with linear algebra. It is rigorous but just enough where it is not overwhelming. It explains the concepts very clearly and the problems range from easy to intermediate level questions. It gives a good mix of computational problems and proofs. Maybe more so on the computational side but that is expected since it is only an introduction. For those who are familiar with linear algebra going on with Axlers, Friedburg, or Hoffman(i like this one) would be a good idea.