Math 102 -- Applied Linear Algebra -- Fall 2017

Lecture site: MANDE B-210
Lecture times: Monday, Wednesday, Friday. 3:00pm-3:50pm.
Discussion sessions B01: Tuesday 5:00p-5:50p, AP&M B412 with Daniel Copeland
B02: Tuesday 6:00p-6:50p, AP&M B412 with Daniel Copeland
B03: Tuesday 7:00p-7:50p, AP&M B412 with Geoff Ganzberger
B04: Tuesday 8:00p-8:50p, AP&M B412 with Geoff Ganzberger
Final Exam
time and place
December 15th, 2017, 3:00pm - 5:59pm. MANDE B-210 and MANDE B-150. Please go to your assigned room on the day of the exam.
Instructor Martin Licht
Email: mlicht AT ucsd DOT edu
Office: AP&M 5880E
Hours: Monday, Wednesday, Friday. 1:50 - 2:50pm.
Teaching Assistant Daniel Copeland
Email: drcopela AT ucsd DOT edu
Office: SDSC 292E
Hours: Wednesday 10:15 - 11:45am, 12:30pm - 2pm.
Teaching Assistant Geoff Ganzberger
Email: gganzber AT ucsd DOT edu
Office: AP&M 6452
Hours: Tuesday 6-7pm, Wednesday 5-7pm, at Muir Woods coffee shop.
Sections 916960, 916961, 916962, 916963
Course content Second course in linear algebra from a computational yet geometric point of view. Elementary Hermitian matrices, Schur's theorem, normal matrices, and quadratic forms. Moore-Penrose generalized inverse and least square problems. Vector and matrix norms. Characteristic and singular values. Canonical forms. Determinants and multilinear algebra.
expected previous knowledge The students are expected to be familiar with the basic concepts of matrix and vector arithmetics, basic knowledge in matrix inversion, and Gaussian elimination.
Resources recommended
in addition
Formal prerequesite Math 18 or Math 20F or Math 31AH, and Math 20C, or consent of instructor.
Credit Hours: 4 units
Homework information Homework will announced on Fridays after lecture. Homework can be submitted to the mailboxes or on Fridays before the lecture, and must be handed-in in handwritten form.
Academic Integrity Every student is expected to conduct themselves with academic integrity. Violations of academic integrity will be treated seriously. See for UCSD Policy on Integrity of Scholarship.


October 11: You are explicitly discouraged from reserving seats. You can only reserve the seat your are sitting on by yourself. On the other hand, if you want to sit down and someone tells you that the seat is "reserved", then you are explicitly encouraged to sit down anyways. Please report any unfair treatment or bullying that you experience or observe to the instructor immediately.

October 16: Homework due on Friday, October 20, must be put into the mailboxes in the basement of AP&M. No homework will be collected in class prior to the first midterm exam.

October 18: The first midterm will take on Friday, October 20, during the usual lecture time. The students are distributed between the usual class room (MANDE B-210) and an overflow room (MANDE B-150), which is located one floor higher. You will be distributed in accordance with your section: Be there and take seats on time!

October 21: This is friendly reminder that my office hours are one hour before the lecture. If you are struggling with the course material, then please contact me or the teaching assistants. If the office hours do not fit your teaching schedule, then a meeting can be scheduled via email.

October 22: A course website has been set up on TritonEd.

October 24: Additional notes on the Fundamental Theorem of Algebra are now available on the course website (see below).

October 26: Additional practice material is now online: Since quite a lot of students are not fully familiar with the irrationality of 2, a classical proof of that fact can be found among the additional material (see below). You should consider it also as a practical demonstration of mathematical reasoning.

November 8: The solutions for the first midterm and selected homeworks are available online.

November 17: The solutions for homework 7 are online. Moreover, a preparation sheet for the second midterm is online.

November 18: The solutions for homework 5 and 6 are online.

November 18: The second midterm will take on Monday, November 20, during the usual lecture time. The students are distributed between the usual class room (MANDE B-210) and an overflow room (MANDE B-150), which is located one floor higher. You will be distributed in accordance with your section: Be there and take seats on time!

November 23: Homework 8 and a bonus homework are available online.

November 23: A Matrix Workout is online for download.

December 11: The final exam will take on Friday, December 15, 3:00pm - 5:59pm. The students are distributed between the usual class room (MANDE B-210) and an overflow room (MANDE B-150), which is located one floor higher. You will be distributed in accordance with your section: Be there and take seats on time!

Grading Information

The final grade will composed 20% homework and either (a) 20% of the first midterm, and 20% of the second midterm, and 40% of the final exam or (b) 20% of the best midterm and 60% of the final exam, depending on what gives the better result.


  1. Homework Assignment 1 - Solutions 1
  2. Homework Assignment 2 - Solutions 2
  3. Homework Assignment 3 - Solutions 3
  4. Preparation for First Midterm - First Midterm - Solutions for First Midterm
  5. Homework Assignment 4 - Solutions 4
  6. Homework Assignment 5 - Solutions 5
  7. Homework Assignment 6 - Solutions 6
  8. Homework Assignment 7 - Solutions 7
  9. Preparation for Second Midterm - Second Midterm - Solutions for Second Midterm
  10. Homework Assignment 8 - Solutions 8
  11. Bonus Homework Assignment
  12. Homework Assignment 9 - Solutions 9
  13. Preparation for Final

Course Calendar

Lecture Content
# 0, 0F
Introduction. Review of Vector Arithmetics. [Leon Ch.1]
# 1, 1M
Review of Vector Arithmetics. Matrices. [Leon Ch.1]
# 2, 1W
Matrix-Vector Product and Matrix Multiplication. [Leon Ch.1]
# 3, 1F
Matrices. Some Examples from Applications. [Leon Ch.1]
# 4, 2M
Matrix Inverse. [Leon Ch.1]
# 5, 2W
Elementary Matrices. Equivalent Conditions for Invertibility.
# 6, 2F
Remarks about triangular matrices. Fields in Algebra with Examples.
# 7, 3M
Complex Numbers.
# 8, 3W
Complex Numbers.
# 9, 3F
First Midterm
#10, 4M
Further Examples for Fields and their Properties.
#11, 4W
Finite Fields.
#12, 4F
Finite Fields. Introduction to Determinants. [Leon, Ch.2]
27.10.2017: Deadline to change grading option, change units, and drop classes without "W" grade on transcript.
#13, 5M
Determinants. Laplace expansion. [Leon, Ch.2]
#14, 5W
#15, 5F
Determinants via Permutations.
#16, 6M
Laplace expansion revisited. [Leon, Ch.2]
#17, 6W
Determinants of elementary matrices. Product formula. [Leon, Ch.2]
#18, 6F
Veteran's Day Holidary
#19, 7M
Cramer's rule. Classical adjunct matrix. [Leon, Ch.2]
#20, 7W
Vector Spaces and Compositions [Leon, Ch. 3 + 4.1]
#21, 7F
Vector Spaces and Compositions [Leon, Ch. 3 + 4.1]
#22, 8M
Second Midterm
#23, 8W
Review of Material.
#24, 8F
Thanksgiving Holiday (Friday).
#25, 9M
Kernel and Range of a Linear Mapping. Linear Combinations. [Slides] [Slides]
#26, 9W
More Results on Linear Combinations and Bases. Dimension. Basis Transformations. [Slides] [Slides]
#27, 9F
Row and Column Space. [Slides]
01.12.2017: Deadline to with "W" grade on transcript.
Similarity Transformations of Matrices. Eigenvalues and Eigenvectors. [Slides] [Slides]
Eigenvalues and Eigenvectors. Continued.
Diagonalization. [Slides]
Final Exam. 3:00pm - 5:59pm. MANDE B-210 and MANDE B-150

Additional Course Material

Notes on the Fundamental Theorem of Algebra
Notes on the Irrationality of the Square Root of 2
Matrix Workout
Notes on the Determinant by James V. Burke
How the Simplex is a Vector Space. By Tom Leinster

Helpful Links

Important academic dates for this academic year