Matrix Algebra SU2025 (4th Term)

This is the course page for Matrix Algebra (Summer 2025, SUM-4 term). This course runs from July 14 to August 14.

Class Hours: Monday, Tuesday, Wednesday, Thursday, Friday 3:00 PM - 4:45 PM in Cupples II, Room 200

Office Hours: Tuesday 4:45 PM - 6:00 PM, Wednesday 4:45 PM - 6:00 PM, Cupples II, Room 200

Lecture/Class Notes:

These notes are what I'm using to organize and prepare myself for class, and they will more or less follow the content of Treil.

Vector Spaces

Linear Transformations

Linear Systems, Rank-Nullity, Matrices of Transformations

Determinants

Eigenvalues, Eigenvectors

Orthogonality, Least Squares

Homework:

Homework 1 (Due 7/21)

Homework 2 (Due 7/30)

Homework 3 (Due 8/7)

The Last One (Due 8/15)

Grading:

Homework will count for 75% of your overall grade. There will be one take-home final that counts for 25% of your grade.

Text: Linear Algebra Done Wrong by Sergei Treil. The plan is to go through Chapters 1-4, and then we will see what time permits.

Topics: 

• Vector spaces

  • Linear combinations, bases, subspaces, linear independence

• Linear transformations

  • Matrices of transformations

  • Invertibility of transformations and matrices

• Systems of linear equations

  • Using the theory of matrices to systematically study solutions of these systems

• Determinants

• Spectral Theory

  • Eigenvalues and eigenvectors

  • Diagonalization

• Inner Products

  • Least Squares