Linear Algebra with Applications, 10th edition

  • Steve Leon, 
  • Lisette de Pillis

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Overview

Linear Algebra with Applications provides a thorough, accessible introduction to linear algebra. It uses modern practical applications to clarify concepts and demonstrate real-world uses, while emphasizing the important role of geometry and visualization in understanding this branch of math.

Published by Pearson (June 3rd 2019) - Copyright © 2020

ISBN-13: 9780135240960

Subject: Advanced Math

Category: 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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