Intro to Linear Algebra

Textbook: There is no textbook. All lecture notes will be posted right here. For further reading I recommend Gilbert Strang's Introduction to Linear Algebra or my lecture notes from a previous iteration of this course.

Office Hours: Mondays 12-1, Thursdays 2-3, and by appointment.
Assignment Due Date Details
Homework 1
Fri, Jan 22 Course Notes
Cartesian Coordinates
Vectors: Algebra vs. Geometry
Length, Distance, Angle
Dot Product
Homework 2
Wed, Feb 3 Course Notes
One Equation = A Shape in Space
System of Equations = Intersection of Shapes
Expected Dimension of the Solution
Parametrizing the Solution
Homework 3
Wed, Feb 17 Course Notes
What is a Hyperplane?
Systems of Linear Equations
The Row Picture and Column Picture
Gaussian Elimination, RREF
Homework 4
Mon, Feb 29 Course Notes
The Matrix Notation: Ax = b
A Matrix is a Function
Matrix Multiplication = Function Composition
Trick for Multiplying Matrices
Exam 1
Review Notes
1A Solutions
1B Solutions
Fri, Mar 4 Total: 30 points
A = 25 and above
B = 21 and above
C = 8 and above
Homework 5
Fri, Mar 25 Course Notes
Fundamental Theorem of Linear Algebra
Existence of Inverse Matrices
Computation of Inverse Matrices
Properties of Matrix Algebra
Homework 6
Wed, Apr 6 Course Notes
Fitting a Line to Data
Projecting a Point onto a Line
Projecting a Point onto a Subspace
Least Squares Approximation
Exam 2
Review Notes
Practice Problems
2A Solutions
2B Solutions
Fri, Apr 15 Total: 30 points
A = 24 and above
B = 16 and above
C = 8 and above
Homework 7
Wed, Apr 20 Course Notes
Fibonacci Numbers
Definition of Eigenvectors & Eigenvalues
The Characteristic Equation
The Idea of Spectral Analysis
Final Exam
Practice Exam
Study Sheet
Wed, Apr 27 2:00-4:30pm