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.