October 17, 2024

Topics

1. Dot product.
2. Angles between vectors.
3. Orthogonal spaces.
4. Orthogonal sets of vectors.
5. Orthogonal matrices.
6. Orthogonal projections.
7. Gram-Schmidt method.
8. QR factorization.

Homework

Projection matrices and leasts squares: jump to timestamp 36:55 directly and watch till the end.

Lecture Notes

Lecture Notes

Exercises

Exercises

Supplementary Content

1. Orthogonal Matrices and Gram-Schmidt (49:09)
2. Dot products and duality (14:11)
3. Systems of linear equations can be seen as projections
4. Orthogonalization by means of elimination
5. Achieving QR with planar rotations