21-241 Matrices and Linear Transformations - CMU Fall 2016 (Sec. F and G)

This is the webpage for Lecture 3 of 21-241 at CMU Fall 2016 semester. I will try to keep it clear and simple.


Laurent Dietrich
Office: Wean Hall 7128
Office Hours: Mondays 4:00-6:00pm


Andrew Zucker
Office: Wean Hall 7207
e-mail: andrewz at andrew dot cmu dot edu
Office Hours: Thursdays 10:30-11:20am


Can be downloaded here.

Schedule and Assignment

Lectures take place on MWF 12:30-1:20pm in Wean Hall 5403.
Recitations for Sec. F on Thursday 09:30-10:20am in Wean Hall 5310 and for Sec. G on 1:30-2:20pm in BH 235A.

If I find a perfect solution among your Assignment, I will sometimes scan it, make it anonymous, and upload it. If you recognize your solution and don't want it to be on my webpage, you can just contact me and I'll take it off.

Week #1
Aug 29 - Sep 2
Assignment | S
M: Systems of linear equations. Vectors.
W: Matrices, row equivalence, operations.
F: Gaussian elimination, reduced row echelon form.
Week #2
Sep 5 - Sep 9
Assignment | S
M: Labor day, no class.
W: Statements, operators, quantifiers, negating a statement, definitions.
F: Theorems, proofs, proof techniques (contraposition, contradiction, induction, cases...)
Week #3
Sep 12 - Sep 16
Assignment | S
M: Abstract vector spaces. Subspaces.
W: Subspaces, spanning sets.
F: Geometry of linear equations in R^n : row by row, column by column, normal form approaches.
Week #4
Sep 19 - Sep 23
Assignment | Sol
M: Vector form and affine spaces.
W: Linear transformations.
F: Matrix algebra: product.
Week #5
Sep 26 - Sep 30
Assignment | Sol | S
M: Matrix algebra: properties, product partitioning, transpose.
W: Review and exercise session.
F: The inverse of a matrix.
Week #6
Oct 3 - Oct 7
Assignment | Sol | S
M: Midterm #1 and solution.
W: Elementary matrices, fundamental theorem of invertible matrices.
F: Columnspace, rowspace, nullspace of a matrix.
Week #7
Oct 10 - Oct 14
Assignment | Sol | S
M: Computing bases of row, column, and nullspaces.
W: Bases, dimension. Rank theorem.
F: Consequences of rank theorem. Coordinates.
Week #8
Oct 17 - Oct 21
Assignment | Sol | S
M: Introduction to eigenvalues.
W: Eigenspaces. Determinant. Laplace's expansion theorem.
F: Mid-semester break, no class.
Week #9
Oct 24 - Oct 28
Assignment | S
M: Elementary row and column operations and determinant.
W: Determinant of a product. Geometrical interpretation of det. Application: polynomial fitting.
F: Back to eigenvalues: existence, properties.
Week #10
Oct 31 - Nov 4
M: Matrix similarity. Diagonalizable matrices.
W: Diagonalization. Application to dynamical systems.
F: Applications.
Week #11
Nov 7 - Nov 11
Assignment | Sol.
M: Midterm #2 and solution.
W: Orthogonality.
F: Orthogonal matrices.
Week #12
Nov 14 - Nov 18
Assignment | Sol.
M: Orthogonal complement. Orthogonal projection.
W: Orthogonal direct sum. The Gram-Schmidt process 1/2.
F: The Gram-Schmidt process 2/2
Week #13
Nov 21 - Nov 25
M: Change of basis matrices.
W: Thanksgiving recess, no class.
F: Thanksgiving recess, no class.
Week #14
Nov 28 - Dec 2
Assignment | Sol.
M: The matrix of a linear transformation (Marco Caroccia).
W: Composition, product.
F: "Similar matrices are matrices of the same transformation in different bases".
Week #15
Dec 5 - Dec 9
M: Orthogonal diagonalization of real symmetric matrices.
W: Review & question session.
F: Review & question session.
Week #16
Dec 12 - Dec 16
M: Final exam and solution.
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