COMS 3251 Fall 2022 (Computational Linear Algebra)

Essential information

• Lectures: Tue/Thu 10:10am–11:25am in Northwest Corner Building 501
• Recitations: Fri 1:00pm–2:00pm in Computer Science Building 480
• Instructor: Daniel Hsu
• Course assistants: Abhinava Sikdar, Albert Jan, Alfonso Velasco, Ari Carter, Eleanor Lin, Lindsey Yang, Samuel Deng, Shreyas Bhat, Xian Jiang

Demos

I have attempted to make these demos work on both tablets with touch input and desktop/laptop computers with a mouse/trackpad.

• Elementary projection operator
• Elementary reflection operator
• Elementary dilation operator
• Shear operator
• Best fitting line

Lecture notes and reading

1. Vectors and linear combinations
   • LAE reading: 1.1
2. Matrix notation and multiplication
   • Examples of matrices from data science
   • LAE reading: 1.4
3. Linear dependence
   • Connectivity in graphs
   • LAE reading: 1.3
4. Elimination and row operations
   • LAE reading: 2.1, 2.2
5. Vector spaces and bases
   • Lagrange interpolation
   • LAE reading: 3.1, 3.4
6. Fundamental subspaces
   • LAE reading: 3.2, 3.3, 3.5
7. Linear transformations and representations
   • LAE reading: 5.3
8. Orthogonality and least squares
   • LAE reading: 1.2, 4.1, 4.2, 4.3, 4.4
9. Singular value decomposition
   • LAE reading: 7.1, 7.2, 7.3 (caveat: the book relies on eigenvectors and eigenvalues to explain SVD)
10. Eigenvectors and eigenvalues
    • LAE reading: 6.1, 6.2, 6.3 (caveat: the book relies on determinants)