Carnegie Mellon

21-241 Matrix Algebra

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Schedule and Assignments

For each week there will be a link to a page with a reading assignment and a homework assignment. This schedule is tentative. It will get more accurate as the semester progresses. No week's topics should be taken as final until the homework is linked.

Week #1:
Aug 28 - Sep 1
M: The Fundamental Problem in Linear Algebra
W: Solutions to Systems of Linear Equations
F: Matrices and Gaussian Elimination
Week #2:
Sep 4 - 8
M: Labor Day: No class.
W: Logic. What is a Proof?
F: What is a Theorem? Techniques of proof.
Week #3:
Sep 11 - 15
M: Vector Spaces
W: Geometry of Linear Equations
F: Linear Transformations
Week #4:
Sep 18 - 22
M: Linear Transformations and Matrices
W: Matrix Operations
F: Representations of Matrix Multipllication
Week #5:
Sep 25 - 29
Exam Review
M: Inverse of a Matrix
W: Finding Matrix Inverses
F: Exam #1 is scheduled for Friday, September 29, from 7:30-8:20AM in McConomy Auditorium.
Week #6:
Oct 2 - 6
M: Properties of the Determinants
W: Cofactor Expansion - Introduction
F: The Laplace Expansion Formula.
Week #7:
Oct 9 - 13
M: The Eigenvalue Problem
W: Properties of Eigenvalues and Eigenvectors
F: Subspaces
Week #8:
Oct 16 - 20
M: Properties of Linear Independence, and Bases
W: Basis and Dimension of Row Spaces
F: Mid-Semester Break. No class.
Week #9:
Oct 23 - 27
M: Dr. Handron is out of town. No Class.
W: Basis and Dimension of Column Spaces and Null Spaces
F: Eigenvalues, Eigenvectors, Eigenspaces, Multiplicity
Week #10:
Oct 30 - Nov 3
Exam Review
M: Exam #2 is scheduled for Monday, October 30, from 7:30-8:20AM in McConomy Auditorium.
M: Makuep Lecture, Orthogonal Vectors and Subspaces
W: Orthogonal Projections
F: The Orthogonal Decomposition Theorem, and Orthogonal Matrices
Week #11:
Nov 6 - 10
M: Orthogonal Matrices. The Gram-Schmidt Process
W: Least Squares Approximations
F: 50th Anniversery Celebration. No class.
Week #12:
Nov 13 - 17
M: Coordinates, Change of Basis
W: Matrix of a Linear Transformation
F: Coordinates in Other Vector Spaces
Week #13:
Nov 20 - 24
Exam Review
M: Exam #3 is scheduled for Monday, November 20, from 7:30-8:20AM in McConomy Auditorium.
W: Thanksgiving Break. No class.
F: Thanksgiving Break. No class.
Week #14:
Nov 27 - Dec 1
M: Coordinate Representations of Linear Transformations
W: Similarity
F: Diagonalization
Week #15:
Dec 4 - 8
M: Orthogonal Diagonalization of Symmetric Matrices
W: Real Symmetric Matrices are Orthogonally Diagonalizable
F: Singular Value Decomposition. Computing the Singular Value Decomposition of a Matrix
Final Exam
Exam Review
The Final Exam has been scheduled for Monday, December 11 from 1:00-4:00pm . The location has not yet been determined. Please take this into account when making your travel plans.