Announcement

• Midterm on Nov 7: in class (10am-11:50am), closed book, one cheat sheet (letter size, double-sided) allowed, exam and sratch papers provided.

• HW5 posted and due Nov 15 @ 11:59pm on Gradescope/BruinLearn.

Q&A

• Affine function. Why? The correspondence between affine functions and $Ax + b$.

• HW2, Q1.

• HW2, Q2, positive definiteness.

• HW3, BV 10.11 a, b.

• HW3, BV 10.36 a.

• HW4, Q5.

• How does Gram-Schmidt algorithm produce QR factorization, esp, when the matrix has linearly dependent columns?

• Difference between QR factorization and rank factorization?

• Draw the four subspaces for an example $A$ and what information can we obtain from the plot?

• Show $||x - y|| \le ||x - z|| + ||z - y||$.

• Show $||A + B|| \le ||A|| + ||B||$.

• How affine function can be written in the form $Ax + b$?

• Explain: $A$ with dim $mxn$ is sparse, between nnz(A) and 2nnz(A) flops, much less than 2mn flops. What does nnz(A) stanford for?

Today

• Review session.

• Office hours.