Matrices and Linear Transformations- Summer I 2012

Acknowledgments

Many thanks to Will Gunther, whose html I blatantly plagiarized to make this page.

Instructor Information

  • Instructor: Paul McKenney
  • Email: pmckenne AT andrew DOT cmu DOT edu
  • Office: Wean 7104
  • Office Hours:
    • Weekdays 1pm-2pm
    • By Appointment

Course Information

  • Course Title: Matrices and Linear Transformations
  • Course Number: 21-241
  • Lecture Room: Wean 4623
  • Lecture Time: 10:30am-11:50am M-F
  • Syllabus: PDF/LaTeX
  • Text: There is no required text to purchase. The following are free things we will use.
  • Optional Resources:
    • Halmos, Paul. Finite Dimensional Vector Spaces. A classic.
  • Prerequisites: There are no formal prerequisites for the course. However, we'll have to use some concepts of mathematics from the course 21-127, Concepts of Mathematics. The following are some suggested (free) resources for these.
    • Sullivan, Brendan. Link to thing Brendan's writing.
    • Simons, L. Chapter Zero. An introduction to the concepts used in Hefferon's book.

Announcements

Course Calendar

Monday Tuesday Wednesday Thursday Friday
21
Notes: PDF/LaTeX
Proofs. Gaussian elimination.
22
Notes: PDF/LaTeX
Matrices.
23
Notes: PDF/LaTeX
Linear transformations.
24
Notes: PDF/LaTeX
HW1: PDF/LaTeX
S1: PDF/LaTeX
Invertible matrices.
25
Notes: PDF/LaTeX
More on invertible matrices.
28
Memorial day.
No class.
29
Notes: PDF/LaTeX
Subspaces. Spanning sets.
30
Notes: PDF/LaTeX
HW2: PDF/LaTeX
S2: PDF/LaTeX
Independent sets.
31
Notes: PDF/LaTeX
Bases. Dimension.
1
Exam 1
Preview: PDF/LaTeX
4
Notes: PDF/LaTeX
The rank + nullity theorem.
5
Notes: PDF/LaTeX
Proof of rank + nullity.
6
Notes: PDF/LaTeX
HW3: PDF/LaTeX
S3: PDF/LaTeX
Problems.
7
Notes: PDF/LaTeX
Multilinear maps.
8
Notes: PDF/LaTeX
The determinant.
11
Notes: PDF/LaTeX
Eigenvalues.
12
Notes: PDF/LaTeX
The inner product.
13
Notes: PDF/LaTeX
HW4: PDF/LaTeX
S4: PDF/LaTeX
Orthogonal bases.
14
Notes: PDF/LaTeX
The Gram-Schmidt process.
15
Exam 2
Preview: PDF/LaTeX
18
Notes: PDF/LaTeX
Multiplicity of an eigenvalue.
19
Notes: PDF/LaTeX
HW5: PDF/LaTeX
S5: PDF/LaTeX
Change of basis.
20
Notes: PDF/LaTeX
Diagonalization.
21
Notes: PDF/LaTeX
More on diagonalization.
22
Notes: PDF/LaTeX
Spectral theory.
25
Notes: PDF/LaTeX
Preliminaries.
26
Notes: PDF/LaTeX
The spectral theorem and corollaries.
27
Notes: PDF/LaTeX
HW6: PDF/LaTeX
S6: PDF/LaTeX
Problems.
28
Notes: PDF/LaTeX
29
Exam 3
Preview: PDF/LaTeX

Note: to compile the LaTeX on this page you will need this style file in the same directory.

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