Linear Algebra with Applications
by Steve Leon, Lisette de Pillis
10th Edition
Publisher: Pearson
Book Details
| Print ISBN | 9780136731634 |
| eText ISBN | 9780135240960 |
| Publisher | Pearson |
| Publishing Year | 2020 |
| Edition | 10th Edition |
| Language | English |
Linear Algebra with Applications, 10th Edition, provides college students with structured instruction in core linear algebra topics. Authored by Steve Leon and Lisette de Pillis, this textbook presents fundamental matrix operations and theoretical concepts for academic study.
The content covers main mathematical subjects starting with matrices and systems of equations, followed by determinants. Subsequent sections explore vector spaces, linear transformations, and orthogonality. Final chapters address eigenvalues, numerical linear algebra, and canonical forms.
Published by Pearson, this 2020 release includes integration with the Pearson+ digital platform. It offers targeted material designed for college students in undergraduate linear algebra courses.
Table of Contents
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 5: Orthogonality
- • 5.1 The Scalar Product in R _n_
- • 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
Chapter 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
Chapter 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
Chapter 8: Canonical Forms
- • 8.1 Nilpotent Operators
- • 8.2 The Jordan Canonical Form
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