Linear Algebra with Applications, Global Edition, 10th edition

Published by Pearson (November 25, 2020) © 2021

  • Steven J. Leon
  • Lisette de Pillis
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£44.99
Instant access

Access details

  • Instant access once purchased
  • Fulfilled by VitalSource
  • For titles accompanied by MyLab/Mastering, this eBook does NOT include access to the platform

Features

  • Add notes and highlights
  • Search by keyword or page

Title overview

This book is for junior/senior-level first courses in linear algebra and assumes calculus as a prerequisite.

This thorough and accessible text, from one of the leading figures in the use of technology in linear algebra, gives students a challenging and broad understanding of the subject. The author infuses key concepts with their modern practical applications to offer students examples of how mathematics is used in the real world. Each chapter contains integrated worked examples and chapter tests. The book stresses the important roles geometry and visualisation play in understanding linear algebra.

Table of contents

  1. Matrices and Systems of Equations 
    • 1.1 Systems of Linear Equations 
    • 1.2 Row Echelon Form
    • 1.3 Matrix Arithmetic
    • 1.4 Matrix Algebra
    • 1.5 Elementary Matrices
    • 1.6 Partitioned Matrices
    • MATLAB Exercises
    • Chapter Test A: True or False
    • Chapter Test B
  2. Determinants
    • 2.1 The Determinant of a Matrix
    • 2.2 Properties of Determinants
    • 2.3 Additional Topics and Applications
    • MATLAB Exercises
    • Chapter Test A: True or False
    • Chapter Test B
  3. Vector Spaces
    • 3.1 Definition and Examples
    • 3.2 Subspaces
    • 3.3 Linear Independence
    • 3.4 Basis and Dimension
    • 3.5 Change of Basis
    • 3.6 Row Space and Column Space
    • MATLAB Exercises
    • Chapter Test A: True or False
    • Chapter Test B
  4. Linear Transformations
    • 4.1 Definition and Examples
    • 4.2 Matrix Representations of Linear Transformations
    • 4.3 Similarity
    • MATLAB Exercises
    • Chapter Test A: True or False
    • Chapter Test B
  5. Orthogonality
    • 5.1 The Scalar Product in Rn
    • 5.2 Orthogonal Subspaces
    • 5.3 Least Squares Problems
    • 5.4 Inner Product Spaces
    • 5.5 Orthonormal Sets
    • 5.6 The Gram–Schmidt Orthogonalization Process
    • 5.7 Orthogonal Polynomials
    • MATLAB Exercises
    • Chapter Test A: True or False
    • Chapter Test B
  6. Eigenvalues
    • 6.1 Eigenvalues and Eigenvectors
    • 6.2 Systems of Linear Differential Equations
    • 6.3 Diagonalization
    • 6.4 Hermitian Matrices
    • 6.5 The Singular Value Decomposition
    • 6.6 Quadratic Forms
    • 6.7 Positive Definite Matrices
    • 6.8 Nonnegative Matrices
    • MATLAB Exercises
    • Chapter Test A: True or False
    • Chapter Test B
  7. Numerical Linear Algebra
    • 7.1 Floating-Point Numbers
    • 7.2 Gaussian Elimination
    • 7.3 Pivoting Strategies
    • 7.4 Matrix Norms and Condition Numbers
    • 7.5 Orthogonal Transformations
    • 7.6 The Eigenvalue Problem
    • 7.7 Least Squares Problems
    • 7.8 Iterative Methods
    • MATLAB Exercises
    • Chapter Test A: True or False
    • Chapter Test B
  8. Canonical Forms
    • 8.1 Nilpotent Operators
    • 8.2 The Jordan Canonical Form
    Appendix: MATLAB
    Bibliography
    Answers to Selected Exercises
    Index

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