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 27 - 31
Assignments
M: The Fundamental Problem in Linear Algebra
W: Solutions to Systems of Linear Equations
F: Matrices and Gaussian Elimination
Week #2:
Sep 3 - 7
M: Labor Day: No class.
W: Logic. What is a Proof?
F: What is a Theorem? Techniques of proof.
Week #3:
Sep 10 - 14
M: Vector Spaces
W: Geometry of Linear Equations
F: Linear Transformations
Week #4:
Sep 17 - 21
M: Linear Transformations and Matrices
W: Matrix Operations
F: Representations of Matrix Multipllication
Week #5:
Sep 24 - 28
M: Inverse of a Matrix
W: Finding Matrix Inverses
F: Exam #1 is scheduled for Friday, September 28, during class time, in McConomy Auditorium.
Week #6:
Oct 1 - 5
M: Properties of the Determinants
W: Cofactor Expansion - Introduction
F: The Laplace Expansion Formula.
Week #7:
Oct 8 - 12
M: The Eigenvalue Problem
W: Properties of Eigenvalues and Eigenvectors
F: Subspaces
Administreative Note: Monday, October 8 is the course drop deadline. Students dropping after this date will receive a grade of W.
Week #8:
Oct 15 - 19
M: Properties of Linear Independence, and Bases
W: Basis and Dimension of Row Spaces
F: Mid-Semester Break. No class.
Week #9:
Oct 22 - 26
M: Basis and Dimension of Column Spaces and Null Spaces
W: Eigenvalues, Eigenvectors, Eigenspaces, Multiplicity
F: Installation of Farnam Jahanian as CMU President. No Class.
Week #10:
Oct 29 - Nov 2
M: Exam #2 will happen at some point.
W: Orthogonal Vectors and Subspaces
F: Orthogonal Projections
Week #11:
Nov 5 - 9
M: The Orthogonal Decomposition Theorem, and Orthogonal Matrices
W: Orthogonal Matrices. The Gram-Schmidt Process
F: Least Squares Approximations
Administreative Note: Tuesday, November 6, is the course withdrawl deadline. Students may not withdraw after this date.
Week #12:
Nov 12 - 16
M: Coordinates, Change of Basis
W: Matrix of a Linear Transformation
F: Exam #3 is scheduled for Friday, November 16, during class time, in McConomy Auditorium.
Week #13:
Nov 19 - 23
M: Coordinate Representations of Linear Transformations
W: Thanksgiving Break. No class.
F: Thanksgiving Break. No class.
Week #14:
Nov 26 - 30
M: Similarity
W: Diagonalization
F: Orthogonal Diagonalization of Symmetric Matrices
Week #15:
Dec 3 - 7
M: Real Symmetric Matrices are Orthogonally Diagonalizable
W: Singular Value Decomposition
F: Computing the Singular Value Decomposition of a Matrix
Final Exam
Exam Review
The Final Exam has not yet been scheduled. The final exam may take place as late as Monday, Dec 17. If you must make travel plans before the final exam schedule is released, make sure they do not require you to leave before Dec 17. Please take this into account when making your travel plans.