Linear Algebra I (Spring 2024)

Welcome to Linear Algebra I! This is a theoretical course covering the fundamentals of linear algebra. In addition to linear algebra, we will cover the basics of mathematical proofs and mathematical writing.

Instructor: Tyler Chen
Email: tyler.chen@nyu.edu
Class: T 5:10-7:00pm (WWH 517)
Office Hours: M,T 12-1pm (WWH905), by appointment

Syllabus
Edstem discussion
Gradescope
Notes

Final Review

Approximate Schedule

Reading are chapters in Lax and Axler.

Week

Topic

Reading

Homework/Quiz

1. (1/23)

Linear spaces, Subspaces

L1, A1A, A1B, A1C

Intro Survey (1/23)

2. (1/30)

span, linear (in)dependence

L1, A2A, A2B, A2C

HW1 (2/5)

3. (2/6)

basis, dimension

L1, A2B, A2C

Q1 (2/6); sample

4. (2/13)

isomorphism, linear maps

L3, A3A, A3B

HW2 (2/19)

5. (2/20)

linear mappings, domain, range, null space

L3, A3A, A3B

6. (2/27)

matrices

L4, A3C

HW3 (3/05)

7. (3/5)

Fundamental theorem, underdetermined linear systems

L3, A3B

8. (3/12)

matrices, quotient space

L2, A3F

HW4 (3/26)

9. (3/19)

SPRING BREAK

10. (3/26)

quotient space, duality

L2, A3F

11. (4/2)

inner product spaces, Gram-Schmidt

HW5 (4/9)

12. (4/9)

orthogonal bases, SVD

13. (4/16)

eigenvalues, eigenvectors, characteristic polynomial, Cayley-Hamilton theorem, diagonalization

HW6 (4/23)

18. (4/23)

Similarity, Spectral Theorem

14. (4/30)

Final exam