Intro to Linear Algebra

Textbook: There is no textbook. I will post all lecture notes on this webpage. For supplementary reading I recommend Gilbert Strang's Introduction to Linear Algebra (any edition).

Lecture: 10:05-11:30 MTuWThF on Zoom
Office Hours: 11:30-12:30 MTuWTh on Zoom

Here is the course syllabus.

Here is an article by Alan Tucker (1993) on The Growing Importance of Linear Algebra in Undergraduate Mathematics. Quote:
This author is personally a bit frustrated that calculus gets all of the first year and half of the second year of the lower-divison core mathematics sequence. Hopefully early in the next century, there will be a 'redistricting' of the lower- division mathematics sequence and linear algebra will get equal time with calculus.
Item Date Information
Homework 1
Fri, May 22 Points vs. Vectors
Vector Arithmetic, Pythagorean Theorem
Lots of Examples
Vector Space Concept, Introduction to Linear Equations
HW1 Discussion, Lines and Hyperplanes
Quiz1 Example
Tues, May 26 20 minutes at the beginning of class
Homework 2
Fri, May 29 Two or Three Lines in 2D, Two Planes in 3D
The Idea of Elimination, Two or Three Planes in 3D
Independence and Dimension, 2 Equations in 4 Unknowns
HW2 Discussion, Determinant of a 2X2 Matrix
Mon, Jun 1 20 minutes at the beginning of class
Homework 3
Fri, June 5 Some Technical Definitions, Gaussian Elimination
Gaussian Elimination on a Computer, Interpreting the RREF
Review of RREF, Definition of Ax=b
Fundamental Theorem of Linear Algebra
HW3 Discussion, FTLA Discussion
Mon, Jun 8 20 minutes at the beginning of class
Homework 4
Fri, June 12 Matrices = Linear Functions
Matrix Multiplication = Composition of Linear Functions
Matrices in Calculus, Matrix Arithmetic
Invertibility of Functions and Matrices
HW4 Discussion, Orthogonal Matrices
Mon, Jun 8 20 minutes at the beginning of class
Homework 5
Mon, June 22 Least Squares Approximation
Projection Onto a Subspace
Review of Projection, Introduction to Diagonalization
Computation of Eigenvalues and Eigenvectors
Linear Systems of Recurrence and Differential Equations
HW5 Discussion, Non-Orthogonal Projections
Tues, June 23 20 minutes at the beginning of class
Discussion and Review Why do we call it Diagonalization?
Complex Numbers, Spectral Theorem, Singular Value Decomposition ...
Final Project
Fri, June 26 Write a summary of what you learned in the course.
Minimum 2 pages, Maximum 10 pages