Linear Algebra, 5th edition

  • Stephen H. Friedberg, 
  • Arnold J. Insel, 
  • Lawrence E. Spence

Your access includes:

  • Search, highlight, and take notes
  • Easily create flashcards
  • Use the app for access anywhere
  • 14-day refund guarantee

$10.99per month

4-month term, pay monthly or pay $43.96

Learn more, spend less

  • Listen on the go

    Learn how you like with full eTextbook audio

  • Special partners and offers

    Enjoy perks from special partners and offers for students

  • Find it fast

    Quickly navigate your eTextbook with search

  • Stay organized

    Access all your eTextbooks in one place

  • Easily continue access

    Keep learning with auto-renew


Linear Algebra presents a careful treatment of the principal topics of the discipline, illustrating the power of linear algebra through practical applications. The text covers the applications of linear algebra to such areas as differential equations, economics, geometry and physics.

Published by Pearson (July 14th 2021) - Copyright © 2019

ISBN-13: 9780137515424

Subject: Advanced Math

Category: Linear Algebra

Table of contents

Table of Contents

* Sections denoted by an asterisk are optional.

  1. Vector Spaces
    • 1.1 Introduction
    • 1.2 Vector Spaces
    • 1.3 Subspaces
    • 1.4 Linear Combinations and Systems of Linear Equations
    • 1.5 Linear Dependence and Linear Independence
    • 1.6 Bases and Dimension
    • 1.7* Maximal Linearly Independent Subsets
    • Index of Definitions
  2. Linear Transformations and Matrices
    • 2.1 Linear Transformations, Null Spaces, and Ranges
    • 2.2 The Matrix Representation of a Linear Transformation
    • 2.3 Composition of Linear Transformations and Matrix Multiplication
    • 2.4 Invertibility and Isomorphisms
    • 2.5 The Change of Coordinate Matrix
    • 2.6* Dual Spaces
    • 2.7* Homogeneous Linear Differential Equations with Constant Coefficients
    • Index of Definitions
  3. Elementary Matrix Operations and Systems of Linear Equations
    • 3.1 Elementary Matrix Operations and Elementary Matrices
    • 3.2 The Rank of a Matrix and Matrix Inverses
    • 3.3 Systems of Linear Equations – Theoretical Aspects
    • 3.4 Systems of Linear Equations – Computational Aspects
    • Index of Definitions
  4. Determinants
    • 4.1 Determinants of Order 2
    • 4.2 Determinants of Order n
    • 4.3 Properties of Determinants
    • 4.4 Summary|Important Facts about Determinants
    • 4.5* A Characterization of the Determinant
    • Index of Definitions
  5. Diagonalization
    • 5.1 Eigenvalues and Eigenvectors
    • 5.2 Diagonalizability
    • 5.3* Matrix Limits and Markov Chains
    • 5.4 Invariant Subspaces and the Cayley–Hamilton Theorem
    • Index of Definitions
  6. Inner Product Spaces
    • 6.1 Inner Products and Norms
    • 6.2 The Gram–Schmidt Orthogonalization Process and Orthogonal Complements
    • 6.3 The Adjoint of a Linear Operator
    • 6.4 Normal and Self-Adjoint Operators
    • 6.5 Unitary and Orthogonal Operators and Their Matrices
    • 6.6 Orthogonal Projections and the Spectral Theorem
    • 6.7* The Singular Value Decomposition and the Pseudoinverse
    • 6.8* Bilinear and Quadratic Forms
    • 6.9* Einstein's Special Theory of Relativity
    • 6.10* Conditioning and the Rayleigh Quotient
    • 6.11* The Geometry of Orthogonal Operators
    • Index of Definitions
  7. Canonical Forms
    • 7.1 The Jordan Canonical Form I
    • 7.2 The Jordan Canonical Form II
    • 7.3 The Minimal Polynomial
    • 7.4* The Rational Canonical Form
    • Index of Definitions


  1. Sets
  2. Functions
  3. Fields
  4. Complex Numbers
  5. Polynomials

Answers to Selected Exercises


Your questions answered

Pearson+ is your one-stop shop, with eTextbooks and study videos designed to help students get better grades in college.

A Pearson eTextbook is an easy‑to‑use digital version of the book. You'll get upgraded study tools, including enhanced search, highlights and notes, flashcards and audio. Plus learn on the go with the Pearson+ app.

Your eTextbook subscription gives you access for 4 months. You can make a one‑time payment for the initial 4‑month term or pay monthly. If you opt for monthly payments, we will charge your payment method each month until your 4‑month term ends. You can turn on auto‑renew in My account at any time to continue your subscription before your 4‑month term ends.

When you purchase an eTextbook subscription, it will last 4 months. You can renew your subscription by selecting Extend subscription on the Manage subscription page in My account before your initial term ends.

If you extend your subscription, we'll automatically charge you every month. If you made a one‑time payment for your initial 4‑month term, you'll now pay monthly. To make sure your learning is uninterrupted, please check your card details.

To avoid the next payment charge, select Cancel subscription on the Manage subscription page in My account before the renewal date. You can subscribe again in the future by purchasing another eTextbook subscription.

Channels is a video platform with thousands of explanations, solutions and practice problems to help you do homework and prep for exams. Videos are personalized to your course, and tutors walk you through solutions. Plus, interactive AI‑powered summaries and a social community help you better understand lessons from class.

Channels is an additional tool to help you with your studies. This means you can use Channels even if your course uses a non‑Pearson textbook.

When you choose a Channels subscription, you're signing up for a 1‑month, 3‑month or 12‑month term and you make an upfront payment for your subscription. By default, these subscriptions auto‑renew at the frequency you select during checkout.

When you purchase a Channels subscription it will last 1 month, 3 months or 12 months, depending on the plan you chose. Your subscription will automatically renew at the end of your term unless you cancel it.

We use your credit card to renew your subscription automatically. To make sure your learning is uninterrupted, please check your card details.