Math 225. Introductory Matrix Theory
Syllabus for Instructors
Text: David C. Lay, Linear Algebra and its Applications, 5th edition, Addison-Wesley, 2016.
(Each section will be covered in about one class hour.)
- Chapter 1: Linear Equations in Linear Algebra
- 1.1 Systems of Linear Equations
- 1.2 Row Reduction and Echelon Forms
- 1.3 Vector Equations
- 1.4 The Matrix Equation Ax=b
- 1.5 Solution Sets of Linear Systems
- 1.6 Applications
- 1.7 Linear Independence
- Chapter 2:
- 2.1 Matrix Operations
- 2.2 The Inverse of a Matrix
- 2.3 Characterizations of Invertible Matrices
- 2.6 The Leontief Input-Output Model
- Chapter 3: Determinants
- 3.1 Introduction to Determinants
- 3.2 Properties of Determinants
- 3.3 Cramer's Rule, Volume, and Linear Transformations
- Chapter 4: Vector Spaces
- 4.1 Vector Spaces and Subspaces
- 4.2 Null spaces, Column Spaces, and Linear Transformations
- 4.3 Linearly Independent Sets: Bases
- 4.5 The Dimension of a Vector Space
- 4.6 Rank
- Chapter 5: Eigenvalues and Eigenvectors
- 5.1 Eigenvalues and Eigenvectors
- 5.2 The Characteristic Equation
- 5.3 Diagonalization
- Chapter 6: Orthogonality and Least Squares
- 6.1 Inner Product, Length, and Orthogonality
- 6.2 Orthogonal Sets
- 6.3 Orthogonal Projections
- 6.5 Least Squares Problems
- 6.6 Applications to Linear Models
Notes:
1. This course should have two midterm exams.
2. The concept of Linear Transformation is not covered in this course.