Linear Algebra 2019 Spring
The material on this webspage accompanies the course
MATH2418.006 at The University of Texas at Dallas.
Textbook:
- Gilbert Strang, Introduction to Linear Algebra, Fifth Edition, Wellesley-Cambridge Press, 2017. ISBN: 978-09802327-7-6.
- Howard Anton, Elementary Linear Algebra, Wiley 11th Edition, 2013. ISBN: 978-1-118-47350-4.
Lecture Notes and Homework:
Introduction to Vectors
Solving Linear Equations
- Vectors and Linear Equations [pdf]
- The Idea of Elimination [pdf]
- Elimination Using Matrices [pdf]
- Rules for Matrix Operations[pdf]
- Inverse Matrices [pdf]
- Elimination = Factorization: A = LU [pdf]
- Transposes and Permutations [pdf]
- Homework 3 [pdf] and Solutions [pdf]
- Homework 4 [pdf] and Solutions [pdf]
- Homework 5 [pdf] and Solutions [pdf]
Vector Spaces and Subspaces
- Spaces of Vectors [pdf]
- NullSapce of A: Solving Ax = 0 and Rx = 0 [pdf]
- The Complete Solution to Ax = b [pdf]
- Independence, Basis and Dimension [pdf]
- Dimensions of the Four Subspaces [pdf]
- Homework 6 [pdf] and Solutions [pdf]
- Homework 7 [pdf] and Solutions [pdf]
- Homework 8 [pdf] and Solutions [pdf]
Orthogonality
- Orthogonality of the Four Subspaces [pdf]
- Projections [pdf]
- Least Squares Approximations [pdf]
- Orthonormal Bases and Gram-Schmidt [pdf]
- Homework 9 [pdf] and Solutions [pdf]
Determinants
- The Properties of Determinants [pdf]
- Permutations and Cofactors [pdf]
- Cramer's Rule, Inverses, and Volumes [pdf]
- Homework 10 [pdf] and Solutions [pdf]
- Homework 11 [pdf] and Solutions [pdf]
Eigenvalues and Eigenvectors
- Introduction to Eigenvalues [pdf]
- Diagonalizing a Matrix [pdf]
- Symmetric Matrices [pdf]
- Positive Definite Matrices [pdf]
- Homework 12 [pdf] and Solutions [pdf]
The Singular Value Decomposition (SVD)
- Bases and Matrices in the SVD [pdf]
- Extra Problems for section 6.5 and 7.2 [pdf] and Solutions [pdf]