Linear Algebra with Applications, 7th Edition

1. Matrices and Systems of Equations.

Systems of Linear Equations. Row Echelon Form. Matrix Algebra. Elementary Matrices. Partitioned Matrices. Matlab Exercises. Chapter Test.

 

2. Determinants.

The Determinant of a Matrix. Properties of Determinants. Cramer's Rule. Matlab Exercises. Chapter Test.

 

3. Vector Spaces.

Definition and Examples. Subspaces. Linear Independence. Basis and Dimension. Change of Basis. Row Space and Column Space. Matlab Exercises. Chapter Test.

 

4. Linear Transformations.

Definition and Examples. Matrix Representations of Linear Transformations. Similarity. Matlab Exercises. Chapter Test.

 

5. Orthogonality.

The Scalar Product in Rn. Orthogonal Subspaces. Least Squares Problems. Inner Product Spaces. Orthonormal Sets. The Gram-Schmidt Orthogonalization Process. Orthogonal Polynomials. Matlab Exercises. Chapter Test.

 

6. Eigenvalues.

Eigenvalues and Eigenvectors. Systems of Linear Differential Equations. Diagonalization. Hermitian Matrices. The Singular Value Decomposition. Quadratic Forms. Positive Definite Matrices. Nonnegative Matrices. Matlab Exercises. Chapter Test.

 

7. Numerical Linear Algebra.

Floating-Point Numbers. Gaussian Elimination. Pivoting Strategies. Matrix Norms and Condition Numbers. Orthogonal Transformations. The Eigenvalue Problem. Least Squares Problems. Matlab Exercises. Chapter Test.

 

8. Iterative Methods. On the website, as pdfs.

 

9. Jordan Canonical Form. On the website, as pdfs.

 

Appendix: MATLAB.

 

Bibliography.

 

Answers to Selected Exercises.

 

Index.