Course Topics

Textbook:

Linear Algebra with Applications (7th edition) by Steven J. Leon

Grading Policy:

In general, there will be two or three mid-term exams, homework, and a final exam. A sample distribution of points is given below.

Sections Covered

1.1: Systems of Linear Equations
1.2: Row Echelon Form
1.3: Matrix Algebra
1.4: Elementary Matrices
1.5: Partitioned Matrices (Optional)
2.1: The Determinant of a Matrix
2.2: Properties of Determinants
2.3: Cramer's Rule
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
4.1: Definition and Examples
4.2: Matrix Representations of Linear Transformations
4.3: Similarity
5.1: The Scalar Product in Rⁿ
5.2: Orthogonal Subspaces
5.3: Least Squares Problems (Optional)
5.4: Inner Product Spaces
5.5: Orthonormal Sets
5.6: The Gram-Schmidt Orthogonalization Process
6.1: Eigenvalues and Eigenvectors
6.4: Hermitian Matrices