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
Assignments M: Labor Day: No class.
W: Logic. What is a Proof?
F: What is a Theorem? Techniques of proof.

Week #3:
Sep 10 - 14
Assignments M: Vector Spaces
W: Geometry of Linear Equations
F: Dr. Handron out of town. No class.

Week #4:
Sep 17 - 21
Assignments M: Linear Transformations
W: Linear Transformations and Matrices
F: Matrix Operations

Week #5:
Sep 24 - 28
Assignments
Exam Review M: Representations of Matrix Multipllication
W: Inverse of a Matrix
F: Exam #1 is scheduled for Friday, September 28, during class time, in McConomy Auditorium.

Week #6:
Oct 1 - 5
Assignments M: Finding Matrix Inverses
W: Properties of the Determinants
F: Cofactor Expansion - Introduction

Week #7:
Oct 8 - 12
Assignments M: The Laplace Expansion Formula.
W: The Eigenvalue Problem
F: Properties of Eigenvalues and Eigenvectors
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
Assignments M: Subspaces
W: Properties of Linear Independence, and Bases
F: Mid-Semester Break. No class.

Week #9:
Oct 22 - 26
Assignments
Exam Review M: Basis and Dimension of Row Spaces
W: Basis and Dimension of Column Spaces and Null Spaces
F: Installation of Farnam Jahanian as CMU President. No Class.

Week #10:
Oct 29 - Nov 2
Assignments Exam #2 will happen at some point during Week #9 or Week #10.
M: Eigenvalues, Eigenvectors, Eigenspaces, Multiplicity
W: Orthogonal Vectors and Subspaces
F: Orthogonal Projections

Week #11:
Nov 5 - 9
Assignments 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
Assignments
Exam Review 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
Assignments M: Coordinate Representations of Linear Transformations
W: Thanksgiving Break. No class.
F: Thanksgiving Break. No class.

Week #14:
Nov 26 - 30
Assignments M: Similarity
W: Diagonalization
F: Orthogonal Diagonalization of Symmetric Matrices

Week #15:
Dec 3 - 7
Assignments 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 been scheduled for Tuesday, December 11 from 5:30-8:30pm in POS A35. Please take this into account when making your travel plans.

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 Assignments	M: Labor Day: No class. W: Logic. What is a Proof? F: What is a Theorem? Techniques of proof.
Week #3: Sep 10 - 14 Assignments	M: Vector Spaces W: Geometry of Linear Equations F: Dr. Handron out of town. No class.
Week #4: Sep 17 - 21 Assignments	M: Linear Transformations W: Linear Transformations and Matrices F: Matrix Operations
Week #5: Sep 24 - 28 Assignments Exam Review	M: Representations of Matrix Multipllication W: Inverse of a Matrix F: Exam #1 is scheduled for Friday, September 28, during class time, in McConomy Auditorium.
Week #6: Oct 1 - 5 Assignments	M: Finding Matrix Inverses W: Properties of the Determinants F: Cofactor Expansion - Introduction
Week #7: Oct 8 - 12 Assignments	M: The Laplace Expansion Formula. W: The Eigenvalue Problem F: Properties of Eigenvalues and Eigenvectors 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 Assignments	M: Subspaces W: Properties of Linear Independence, and Bases F: Mid-Semester Break. No class.
Week #9: Oct 22 - 26 Assignments Exam Review	M: Basis and Dimension of Row Spaces W: Basis and Dimension of Column Spaces and Null Spaces F: Installation of Farnam Jahanian as CMU President. No Class.
Week #10: Oct 29 - Nov 2 Assignments	Exam #2 will happen at some point during Week #9 or Week #10. M: Eigenvalues, Eigenvectors, Eigenspaces, Multiplicity W: Orthogonal Vectors and Subspaces F: Orthogonal Projections
Week #11: Nov 5 - 9 Assignments	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 Assignments Exam Review	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 Assignments	M: Coordinate Representations of Linear Transformations W: Thanksgiving Break. No class. F: Thanksgiving Break. No class.
Week #14: Nov 26 - 30 Assignments	M: Similarity W: Diagonalization F: Orthogonal Diagonalization of Symmetric Matrices
Week #15: Dec 3 - 7 Assignments	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 been scheduled for Tuesday, December 11 from 5:30-8:30pm in POS A35. Please take this into account when making your travel plans.