Announcements

• HW8 due Dec 2 @ 11:59pm.

• Today’s (Thu, 12/1) office hours: 2pm-3pm. On Zoom: https://ucla.zoom.us/j/91248926778

• Final week office hours (changed): Tue (12/6) 10am-12pm, Thu (12/8) 10am-12pm. Zoom: https://ucla.zoom.us/j/91248926778

• Teaching evaluation (if you haven’t done so). https://my.ucla.edu/

• Homework feedback

  • HW6: Q7(2): all solutions can be characterized as ``a particular solution + any vectors in the null space”. Q7(3): exclude the possibility of zero solution; we don’t have the essential disjointness of column space and null space, unless it’s a symmetric matrix; if there’s a non-zero solution, then $u$ is in the column space and thus a linear combination of $v$ and $w$, conflicting with the linear independence.

  • HW6 Q8: $A$ may not be a square matrix. Need to show $Ax \ne 0$ for any $x \ne 0$.

  • HW6 Q10: need to show that the Rayleigh quotient achieves the maximal value.

  • HW7 Q1.

  • HW7 Q2.3 orthogonal projector.

  • HW7 Q3.

• FAQs

  • HW8 Q2.

  • HW8 Q1: How to use Cholesky factor to check optimality of sigma/covariance matrix

  • HW8 Q4.2: how to use the SVD of $\tilde{Y}^T \tilde{X}$?

  • HW8 Q6.1 part 3 and 4 (can you also redo part 1 and 2 also?)

• Tips for surviving graduate coursework

  • Start hw early. Time your work.

  • Use every office hour.

  • Ask questions in class and in office hours.

  • Learn to typeset math (Quardro, RMarkdown, Jupyter Notebook, LaTeX). Treat homework as writing exercises.