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Linear Algebra with Applications, 10th edition

Published by Pearson (February 21, 2020) © 2020

  • Steve Leon
  • Lisette de Pillis

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For sophomore, junior or senior-level first courses in linear algebra

A thorough, accessible introduction

Linear Algebra with Applications, 10th Edition encourages a challenging and broad understanding of the subject. A leader in using technology for linear algebra, Leon is joined by new co-author Lisette de Pillis, who brings her passion for teaching and solving real-world problems to this revision. Transformed from print to an eText, it is packed with interactive figures and much more. Each chapter contains integrated worked examples, practical applications, computer exercises and chapter tests. The roles of geometry and visualization in understanding linear algebra are emphasized.

Hallmark features of this title

  • Extensive applications of linear algebra concepts to a variety of real-world situations show how theories and concepts of linear algebra can help solve modern-day problems.
  • Abundant computer exercises help students visualize and discover linear algebra, and explore more realistic applications that are too computationally intensive to work out by hand. These exercises also give students experience in performing matrix computations.
  • Worked-out examples illustrate new concepts, making the material less abstract.
  • 2 chapter tests  for every chapter help students study for exams and get the practice they need to master the material.
  • A comprehensive MATLAB®  appendix gives users all the information they need to use the latest version of MATLAB. 

New and updated features of this title

  • Transformed from print to a digital-based tool, the 10th Edition is packed with features such as interactive figures that bring content to life. A loose-leaf, 3-hole punched print version is available if needed.
  • Portability: The eText delivers the same experience on mobile devices, tablets and computers. Portable access lets students read their eText at their convenience, on Android and iOS mobile phones and tablets; students also can read offline when necessary.
  • Ease of use:  Straightforward setup makes it easy for instructors to get their class up and reading quickly on the first day of class. In addition, LMS integration provides institutions, instructors, and students with single sign-on access to the eText via many popular learning management systems.

Features of Pearson eText for the 10th Edition

  • Interactive figures and utilities  provide opportunities for students to interact with content in a dynamic manner to build or enhance understanding. Interactive figures allow students to explore concepts geometrically in ways that are not possible without technology. 
  • Assessment exercises are set up to allow students to enter answers and get immediate feedback; these exercises are of the “self-check” variety.
  • Hints are included for selected exercises.
  • Notes, Labels and  Highlights: Notes allow instructors to add their personal teaching style to important topics, call out need-to-know information, or clarify difficult concepts. Students can make their eText their own by creating highlights with meaningful labels and notes, helping them focus on what they need to study. The customizable Notebook allows students to filter, arrange, and group their notes in a way that makes sense to them.
  • With the  dashboard,  instructors can create reading assignments and see the time spent in the eText to help plan more effective instruction.
  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

About our authors

Steven J. Leon is a Chancellor Professor Emeritus at the University of Massachusetts Dartmouth. He has been a Visiting Professor at Stanford University, ETH Zurich (the Swiss Federal Institute of Technology), KTH (the Royal Institute of Technology in Stockholm), UC San Diego, and Brown University. His areas of specialty are linear algebra and numerical analysis.

Leon has been active in the International Linear Algebra Society (ILAS).  He served as Editor-in-Chief of Image, the Bulletin of the International Linear Algebra Society from 1989 to 1997. He also served two terms as Chair of the ILAS Education Committee. In the 1990's he served as Director of the NSF sponsored ATLAST Project (Augmenting the Teaching of Linear Algebra using Software Tools). The project conducted 18 regional faculty workshops during the period from 1992–1997.

Professor Leon is now living in San Diego, where he remains professionally active and participates in the Computational Mathematics seminars at UCSD.

Lisette de Pillis holds the Norman F. Sprague chaired Professorship in the Life Sciences, and is department chair and a professor of mathematics at Harvey Mudd College. De Pillis has also been the director of the Harvey Mudd College Global Clinic Program and the Director for the Center for Quantitative Life Sciences.

De Pillis is a Fellow of the American Mathematical Society, an Argonne National Laboratory Maria Goeppert-Mayer Distinguished Scholar, and a HERS-CBL Clare Booth Luce Leadership in STEM Scholar. She has been an officer of the Society for Mathematical Biology, a guest editor for the MAA American Mathematical Monthly, an Editorial Board Member for the AMS Notices, Associate Editor for the Undergraduate Mathematics Applications Project, and a Board Member for Springer Undergraduate Texts in Mathematics.

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