Math 221 Linear Algebra
Oxford College of Emory University, Fall 2020
Oxford College of Emory University, Fall 2020
Elementary Linear Algebra: Applications Version by Howard Anton & Chris Rorres, 11th Edition.
MATLAB
Chapter 1 System of Linear Equations and Matrices
1.1 Introduction to Systems of Linear Equations
1.2 Gaussian Elimination
1.3 Matrices and Matrix Operations
1.4 Inverses; Algebraic Properties of Matrices
1.5 Elementary Matrices and a Method for Finding A^-1
1.6 More on Linear Systems and Invertible Matrices
1.7 Diagonal, Triangular, and Symmetric Matrices
1.8 Matrix Transformations
Chapter 2 Determinants
2.1 Determinants by Cofactor Expansion
2.2 Evaluating Determinants by Row Reduction
2.3 Properties of Determinants; Cramer's Rule
Chapter 3 Euclidean Vector Spaces
3.1 Vectors in 2-Space, 3-Space, and n-Space
3.2 Norm, Dot Product, and Distance in R^n
3.3 Orthogonality
3.4 The Geometry of Linear Systems
3.5 Cross Product
Chapter 4 General Vector Spaces
4.1 Real Vector Spaces
4.2 Subspaces
4.3 Linear Independence
4.4 Coordinates and Basis
4.5 Dimension
4.6 Change of Basis
4.7 Row Spacde, Column Space, and Null Space
4.8 Rank, Nullity, and the Fundamental Matrix Spaces
4.10 Properties of Matrix Transformations
Chapter 5 Eigenvalues and Eigenvectors
5.1 Eigenvalues and Eigenvectors
5.2 Diagonalization
Additional Topic: Cayley--Hamilton Theorem for Matrices
Chapter 6 Inner Product Spaces
6.1 Inner Products
6.2 Angle and Orthogonality in Inner Product Spaces
6.3 Gram--Schmidt Process; QR-Decomposition
Chapter 7 Diagonalization and Quadratic Forms
7.1 Orthogonal Matrices
7.2 Orthogonal Diagonalization
Chapter 8 General Linear Transformations
8.1 General Linear Transformations
8.2 Compositions and Inverse Transformations
8.3 Isomorphism
8.4 Matrics for General Linear Transformations
8.5 Similarity
Chapter 9 Numerical Methods
9.1 LU-Decomposition