Linear Algebra

Fall 2017

Instructor: Matt Kerr
Office: Cupples I, Room 114
e-mail: matkerr [at]
Office Hours: Tuesday 12-1, Thursday 3-4, and by appointment


Math 310 or permission of instructor. Math 309 is not an explicit prerequisite, but familiarity with basic topics from matrix theory (matrix operations, linear systems, row reduction, Gaussian elimination) is expected, as these will be covered quickly.

Class Schedule:

Lectures are on Monday, Wednesday, and Friday from 12-1 in Crow 206, beginning Monday Aug. 28 and ending with a final exam review class on Friday Dec. 8. Note that Monday Sep. 4, Monday Oct. 16, Wednesday Nov. 22, and Friday Nov. 24 are holidays.

Midterm Exam 1: Wednesday, Oct. 11 [solutions]
Midterm Exam 2: Friday, Nov. 10 [solutions]
Final Exam: Wednesday, Dec. 20, 10:30-12:30 [solutions]

Regarding missed exams, see the Grading Policy section below. Calculators aren't allowed, but the exams will not be computationally heavy.


I encourage you to obtain a copy of:

Friedberg, Insel, and Spence, "Linear Algebra (4th Ed.)", Pearson, 2003;

but I will also post my lecture notes on-line (and those will be our primary text).

Course Syllabus:

Introduction to the linear algebra of finite-dimensional vector spaces. A brief outline:

I. Linear Systems
II. Vector Spaces
III. Linear Transformations
IV. Determinants
V. Eigenvectors and Eigenvalues
VI. Canonical Forms
VII. Inner Products and Spectral Theory


There will be a weekly homework due by 6 PM on Friday, consisting of the problems at the end of the sections identified below. You will submit these through Crowdmark, via the personalized e-mail link you will receive for each assignment. I am available for help in office hours. (Regarding late homework, cf. the Grading Policy below.)

Problem Set 1: (I.A,B) (due Friday Sep. 1) [solutions]
Problem Set 2: (I.C,D) and (II.A) (due Friday Sep. 8) [solutions]
Problem Set 3: (II.B,C) (due Friday Sep. 15) [solutions]
Problem Set 4: (II.D,E) and (III.A) (due Friday Sep. 23) [solutions]
Problem Set 5: (III.B-D) (due Friday Sep. 30) [solutions]
Problem Set 6: (IV.A-B) (due Friday Oct. 6) [solutions]
Problem Set 7: (IV.C) and (V.A-B) (due Friday Oct. 20) [solutions]
Problem Set 8: (V.C) (due Friday Oct. 27) [solutions]
Problem Set 9: (VI.A-B) (due Friday Nov. 3) [solutions]
Problem Set 10: (VI.C-E) (due Friday Nov. 17) [solutions]
Problem Set 11: (VII.A-D) (due Friday Dec. 1) [solutions]
Problem Set 12: (VII.D-E) (due Friday Dec. 8) [solutions]

Lecture Notes:

Will be posted below on the day of the lecture. The hope is that this will make note-taking optional.

I. Linear Systems
A. Geometry of linear systems
B. Gauss-Jordan elimination
C. Matrix algebra
D. Solving linear systems via row-reduction

II. Vector Spaces
A. Vector spaces and subspaces
B. Basis and dimension
C. A "nice" basis for subspaces of Rn
D. There is exactly one rref matrix row-equivalent to any A
E. Coordinates

III. Linear Transformations
A. Linear transformations without matrices
B. Linear transformations in terms of matrices
C. Linear functionals I: Derivations and Jacobians
D. Linear functionals II: the dual space
IV. Determinants
A. Alternating multilinear functionals
B. Computational methods for determinants
C. Properties and applications of determinants
V. Eigenvectors and Eigenvalues
A. Linear dynamical systems
B. Mechanics and theory of diagonalization
C. Complex eigenvalues and other topics
VI. Canonical Forms
A. On the minimal polynomial of a transformation
B. Normal form of a (polynomial) matrix
C. Rational canonical form
D. Generalized eigenspaces
E. Jordan normal form
VII. Inner Products and Spectral Theory
A. Review of orthogonality
B. Bilinear forms
C. Inner products
D. The spectral theorem
E. The singular value decomposition
F. Fourier series

Grading Policy:

Homework is worth 40% of your final grade; Midterm Exam 1 and Midterm Exam 2 are worth 15% each; and the Final Exam is worth 30%. I will drop your lowest 2 homework scores. Grades will be kept track of on blackboard.

If you have to miss an hour exam for a legitimate reason, you will be given a makeup exam. Of course verified illness and serious family emergency are legitimate reasons. (For the final exam, those are the only acceptable reasons.) Regarding other conflicts, e-mail me as soon as you know about them.

In general, credit will be given for late homework only in the event of illness or emergency. If you can't make it to class on a Friday to hand it in, send it with a trusted friend or slip it under my door the day or the morning before class.

You may discuss homework with other students (calculators are of course also allowed), but you should not have duplicate solutions. This link takes you to the standard university policies on academic integrity.