Linear Algebra with Applications, 10th edition

  • Steve Leon, 
  • Lisette de Pillis

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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
Answers to Selected Exercises

Your questions answered

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