# 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

• 6/7: There were a couple typos in homework 4 (in problems 5 and 6), and problem 4 was completely wrong. I've corrected all that.
• 6/11: There were typos in the solutions to Homework 2 (problems 1,2, and 6). I've fixed those.
• 6/12: Yet more typos! This time in the Exam 2 preview, problem 5; when taking the product of permutation matrices, the order of composition reverses. It's been corrected. I've also added a little to yesterday's notes. (I'll talk about the extra stuff today.)
• 6/17: I've put up (partial) solutions for homework 4, including solutions to all of the abstract problems.
• 6/22: The Exam 3 preview is (finally) up.
• 6/25: There was a slight typo in HW6 #7 (I didn't specify that you're only considering the real eigenvalues). I've also extended the hint for 6(b)-> 6(c).
• 6/26: There was another typo in HW6, this time in #12; the matrix should be size n x n (it was (n + 1) x (n + 1)).

## Course Calendar

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

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