21-241 Matrix Algebra


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Schedule and Homework

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:
Jan 11 - 15
Homework M: Introduction (1.1)
W: The Geometry of Linear Equations (1.2)
F: An Example of Gaussian Elimination (1.3)

Week #2:
Jan 18 - 22
Homework M: Matrix Notation and Matrix Multiplication (1.4)
W: Triangular Factors and Row Exchanges (1.5)
F: Inverses and Transposes (1.6)

Week #3:
Jan 25 - 29
Homework M: Special Matrices and Applications (1.7)
W: Vector Spaces and Subspaces (2.1)
F: Solving Ax=0 and Ax=b (2.2)

Week #4:
Feb 1 - 5
Homework M: Linear Independence, Basis and Dimension (2.3)
W: Linear Independence, Basis and Dimension (2.3)
F: The Four Fundamental Subspaces (2.4)

Week #5:
Feb 8 - 12
Homework
Exam Review M: Snow Day!
W: Snow Day!
F: Linear Transformations (2.6)

Week #6:
Feb 15 - 19
Homework M: Linear Transformations (2.6)
W: Orthogonal Vectors and Subspaces (3.1)
F: Orthogonal Vectors and Subspaces (3.1)

Week #7:
Feb 22 - 26
Homework
Exam Review M: Cosines and Projections onto Lines (3.2)
W: Exam #1
F: Projections and Least Squares (3.3)

Week #8:
Mar 1 - 5
Homework M: Projections and Least Squares (3.3)
W: Orthogonal Bases and Gram-Schmidt (3.4)
F: Mid-Semester Break. No Class.

Spring Break:
Mar 8 - 12 Spring Break!

Week #9:
Mar 15 - 19
Homework M: Orthogonal Bases and Gram-Schmidt (3.4)
W: The Fast Fourier Transform (3.5)
F: Determinants: Introduction (4.1)

Week #10:
Mar 22 - 26
Homework M: Properties of the Determinant (4.2)
W: Formulas for the Determinant (4.3)
F: Applications of the Determinant (4.4)

Week #11:
Mar 29 - Apr 2
Homework M: Eigenvalues and Eigenvectors: Introduction (5.1)
W: Diagonalization of a Matrix (5.2)
F: Diagonalization of a Matrix (5.2)

Week #12:
Apr 5 - 9
Homework M: Difference Equations and Powers A^k (5.3)
W: Difference Equations and e^At (5.4)
F: Complex Matrices (5.5)

Week #13:
Apr 12 - 16
Homework M: Similarity Transformations (5.6)
W: Similarity Transformations (5.6)
F: Spring Carnival: No Class.

Week #14:
Apr 19 - 23
review problems M: Minima, Maxima and Saddle Points (6.1)
W: Exam #3 - Tentative
F: Tests for Positive Definiteness (6.2)

Week #15:
Apr 26 - 30
Homework M: Singular Value Decomposition (6.3)
W: Minimum Principles (6.4)
F:

Final Exam
review problems The Final Exam has not yet been scheduled. The final exam may take place as late as Tuesday, May 11. If you must make travel plans before the final exam schedule is released, make sure they do not require you to leave before May 12.

Week #1: Jan 11 - 15 Homework	M: Introduction (1.1) W: The Geometry of Linear Equations (1.2) F: An Example of Gaussian Elimination (1.3)
Week #2: Jan 18 - 22 Homework	M: Matrix Notation and Matrix Multiplication (1.4) W: Triangular Factors and Row Exchanges (1.5) F: Inverses and Transposes (1.6)
Week #3: Jan 25 - 29 Homework	M: Special Matrices and Applications (1.7) W: Vector Spaces and Subspaces (2.1) F: Solving Ax=0 and Ax=b (2.2)
Week #4: Feb 1 - 5 Homework	M: Linear Independence, Basis and Dimension (2.3) W: Linear Independence, Basis and Dimension (2.3) F: The Four Fundamental Subspaces (2.4)
Week #5: Feb 8 - 12 Homework Exam Review	M: Snow Day! W: Snow Day! F: Linear Transformations (2.6)
Week #6: Feb 15 - 19 Homework	M: Linear Transformations (2.6) W: Orthogonal Vectors and Subspaces (3.1) F: Orthogonal Vectors and Subspaces (3.1)
Week #7: Feb 22 - 26 Homework Exam Review	M: Cosines and Projections onto Lines (3.2) W: Exam #1 F: Projections and Least Squares (3.3)
Week #8: Mar 1 - 5 Homework	M: Projections and Least Squares (3.3) W: Orthogonal Bases and Gram-Schmidt (3.4) F: Mid-Semester Break. No Class.
Spring Break: Mar 8 - 12	Spring Break!
Week #9: Mar 15 - 19 Homework	M: Orthogonal Bases and Gram-Schmidt (3.4) W: The Fast Fourier Transform (3.5) F: Determinants: Introduction (4.1)
Week #10: Mar 22 - 26 Homework	M: Properties of the Determinant (4.2) W: Formulas for the Determinant (4.3) F: Applications of the Determinant (4.4)
Week #11: Mar 29 - Apr 2 Homework	M: Eigenvalues and Eigenvectors: Introduction (5.1) W: Diagonalization of a Matrix (5.2) F: Diagonalization of a Matrix (5.2)
Week #12: Apr 5 - 9 Homework	M: Difference Equations and Powers A^k (5.3) W: Difference Equations and e^At (5.4) F: Complex Matrices (5.5)
Week #13: Apr 12 - 16 Homework	M: Similarity Transformations (5.6) W: Similarity Transformations (5.6) F: Spring Carnival: No Class.
Week #14: Apr 19 - 23 review problems	M: Minima, Maxima and Saddle Points (6.1) W: Exam #3 - Tentative F: Tests for Positive Definiteness (6.2)
Week #15: Apr 26 - 30 Homework	M: Singular Value Decomposition (6.3) W: Minimum Principles (6.4) F:
Final Exam review problems	The Final Exam has not yet been scheduled. The final exam may take place as late as Tuesday, May 11. If you must make travel plans before the final exam schedule is released, make sure they do not require you to leave before May 12.