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Fall 2026
Honors Linear Algebra
AS.110.212 (01)
Name: Professor Mee Seong Im
Room: Hodson 315
Dates: Monday Aug 31, 2026 - Friday Dec 11, 2026
Time: Mondays and Wednesdays 1:30 - 2:45 pm
Office Hours: Mondays, 3 - 4 pm, Wednesdays 3 - 4 pm in Krieger 419
Teaching Assistant:
Anna Matsui
Room: Hodson 315
Recitation: Fridays 1:30 - 2:20 pm
Office Hours: Thursdays, 2 - 3 pm in Krieger 204
Course Textbooks.
Linear Algebra (5th Edition), by Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence
Linear Algebra Done Right (3rd Edition), by Sheldon Axler (supplementary textbook)
On Mondays and Wednesdays, you will have lectures in Hodson 315.
On Fridays, you will have recitation sections with Anna Matsui in Hodson 315.
Departmental policy: cell phones are NOT allowed during class or during the recitation sections.
Collaboration and discussions on homework sets are encouraged, but please do your own write-up of the examples and the proofs.
I will drop two lowest HW, Friday's in-class participation, and quiz grades. So make-up work will not be allowed.
Breakdown of Grades.
10% Homework (due: Fridays at 1:30 pm, give to the TA; 2 lowest HW grades will be dropped)
10% In-class participation (Friday's TA section; 2 lowest participation grades will be dropped)
25% Quizzes (Fridays, no books, notes, or technology; 2 lowest quiz grades will be dropped)
35% In-class midterm (no books, notes, technology, or friends)
20% End-of-the-semester presentations
Projects.
20 minutes each, 3 minutes Q&A, 2-minute break/transition between the presentations.
No slides. Chalkboard presentations only.
More details later.
Grading Scale.
A: 90 - 100
B: 80 - 89
C: 70 - 79
D: 63 - 69
F: < 63
"+" and "-" will be determined at the end of the semester.
Mathematica.
Please install it via JHU's website.
Schedule.
Mon August 31: Vectors and vector spaces, and their proofs (Sections 1.1 and 1.2)
Homework 1, due Friday September 4, 2026
Wed September 2: Subspaces and direct sums (Sections 1.2 and 1.3)
Homework 2, due Friday September 11, 2026
Wed September 9: Span, linear combinations, systems of linear equations, and linear independence (Sections 1.3, 1.4, and 1.5)
Homework 3, due Friday September 18, 2026
Mon September 14: Bases and dimension (Sections 1.5 and 1.6)
Wed September 16: Linear transformations, null spaces, and ranges (Sections 1.6 and 2.1)
Homework 4, due Friday September 25, 2026
Mon September 21: Linear transformations, null spaces, and ranges (Section 2.1)
Wed September 23: Linear transformations, null spaces, and ranges and the matrix representation of a linear transformation (Sections 2.1 and 2.2)
Homework 5, due Friday October 2, 2026
Mon September 28: The matrix representation of a linear transformation and composition of linear transformations (Sections 2.2 and 2.3)
Wed September 30: Invertibility and isomorphisms (Section 2.4)
Mon October 5:
Wed October 7:
Mon October 12:
Wed October 14:
Mon October 19: Diagonalization
Wed October 21: Inner product spaces
Thurs - Fri October 22 - 23: Fall break; no classes
Mon October 26:
Wed October 28: Midterm
Mon November 2:
Wed November 4: Einstein's special theory of relativity and conditioning, and the Rayleigh quotient
Mon November 9: Geometry of orthogonal operators
Wed November 11:
Mon November 16:
Wed November 18: Jordan canonical form, minimal polynomial, rational canonical form
Mon - Fri November 23 - 27: Fall recess (Thanksgiving week); no classes
Mon November 30: Geometry of commuting and almost-commuting matrices
Wed December 2: Presentations
Mon December 7: Presentations
Wed December 9: Presentations
Wed December 23, 2:00 - 5:00pm: Final Exam
Remarks.
Wednesday Sept 9, 2026.
Hi everyone,
I realized that I didn't make the direct sum notation from today's class clear (the oplus notation, it's the plus sign with a circle around it). This is from Section 1.3.
The notation V = W_1 \oplus W_2 (W_1 direct sum W_2) means by definition that V is a vector space because it is constructed from other vector (sub)spaces W_1 and W_2.
So if you write V = W_1 \oplus W_2, then every single vector v in V can be written as the sum of a vector w_1 from W_1 and w_2 from W_2.
So v = w_1 + w_2.
The condition W_1 cap W_2 = {0} means the two subspaces (vector spaces) are independent; they do not have nontrivial overlap. They overlap only at the zero vector.
Because of these two conditions, every vector in V can be written in exactly one unique way, as a sum of an element from W_1 and an element from W_2.
The direct sum notation is interesting because it gives you a way to build larger vector spaces out of smaller pieces. Or you can break down a large vector space into smaller independent components.
Both of these questions arise in what is known as Representation Theory.
I hope this is helpful,
Mee Seong
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