Linear Algebra with Applications, 10th edition

Published by Pearson (June 3, 2019) © 2020

  • Steve Leon
  • Lisette de Pillis

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ISBN-13: 9780135240960 (2019 update)
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Now delivered digitally, Linear Algebra with Applications is a thorough, accessible introduction to linear algebra that encourages a challenging and broad understanding of the subject. A leading figure in using technology for linear algebra, Steve Leon is now joined by new co-author Lisette de Pillis, who brings her passion for teaching and solving real-world problems to the 10th Edition. Transformed from print to a digital-based tool, it is packed with features such as interactive figures that bring content to life. This change in format supports the authors' hallmark of using modern practical application to make key concepts tangible and demonstrating how mathematics is used in the real world. Each chapter contains integrated worked examples, practical applications, computer exercises and chapter tests. The important roles played by geometry and visualization in understanding linear algebra are emphasized. Calculus is assumed as a prerequisite.

  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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