Math 221 Vectors and Matrices

Textbook: 

• Elementary Linear Algebra: A Matrix Approach by Stephen Spence, Lawrence Instel, and Arnold Friedberg, 2nd Edition.

Software:

ChatGPT & MATLAB

Topics:

Chapter 1 Matrices, Vectors, and Systems of Linear Equations

1.1 Matrices and Vectors
1.2 Linear Combinations, Matrix-Vector Products, and Special Matrices
1.3 System of Linear Equations
1.4 Gaussian Elimination
1.6 The Span of a Set of Vectors
1.7 Linear Dependence and Linear Independence

Chapter 2 Matrices and Linear Transformations

2.1 Matrix Multiplication
2.3 Invertibility and Elementary Matrices
2.4 The Inverse of a Matrix
2.6 The LU Decomposition of a Matrix
2.7 Linear Transformations and Matrices
2.8 Composition and Invertibility of Linear Transformations

Chapter 3 Determinants

3.1 Cofactor Expansion
3.2 Properties of Determinants

Chapter 4 Subspaces and Their Properties

4.1 Subspaces
4.2 Basis and Dimension
4.3 The Dimension of Subspaces Associated with a Matrix
4.4 Change of Basis* (One conic section example, including change of basis, eigenvalues, eigenvectors, and orthogonal matrices)

Chapter 5 Eigenvalues, Eigenvectors, and Diagonalization

5.1 Eigenvalues and Eigenvectors
5.2 The Characteristic Polynomial
5.3 Diagonalization of Matrices
Additional Topic: Cayley--Hamilton Theorem for Matrices

Chapter 6 Orthogonality

6.1 The Geometry of Vectors
6.2 Orthogonal Vectors (QR Decomposition)