Linear Algebra with Applications, Global Edition

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
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Determinants

2.1 The Determinant of a Matrix
2.2 Properties of Determinants
2.3 Additional Topics and Applications
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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
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Linear Transformations

4.1 Definition and Examples
4.2 Matrix Representations of Linear Transformations
4.3 Similarity
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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
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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
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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
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Canonical Forms

8.1 Nilpotent Operators
8.2 The Jordan Canonical Form

Appendix: MATLAB Bibliography Answers to Selected Exercises Index