# 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

**3.** (2/6)

basis, dimension

L1, A2B, A2C

**4.** (2/13)

isomorphism, linear maps

L3, A3A, A3B

**5.** (2/20)

linear mappings, domain, range, null space

L3, A3A, A3B

Q2

**6.** (2/27)

matrices

L4, A3C

**7.** (3/5)

Fundamental theorem, underdetermined linear systems

L3, A3B

Q3

**8.** (3/12)

matrices, quotient space

L2, A3F

**10.** (3/26)

quotient space, duality

L2, A3F

Q4

**11.** (4/2)

inner product spaces, Gram-Schmidt

A6

**12.** (4/9)

orthogonal bases, SVD

L6

Q5

**13.** (4/16)

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

L5

**18.** (4/23)

Similarity, Spectral Theorem

L6

Q6