Announcement

Feedback on HW7

  • See Tomoki’s feedback on Slack.

Q&A

  • Summary of matrix decompositions: LU, Cholesky, QR, spectral decomposition, SVD. When to use what?

  • HW5 Q2.6, HW6 Q3.5.

  • SVD exercises, HW5: Q1.3, Q1.4, Q3.1, HW7 Q3.6. BV: 12.4(c), 12.8(b).

  • HW7 Q3.6

  • Could you cover any quick tips and tricks of finding eigenvalues (for instance, if it’s a diagonal matrix, if the columns are dependent, etc.)? I’m also a little confused on when an eigenvalue for a matrix is repeated, and was wondering if you could clarify that and what it means (such as if there’s any significance to it beyond having a repeated root).

  • In the eigen-decomposition lecture, why must (λI − A)x = 0, λI − A be singular and det(λI − A) = 0?

  • Can eigen-decomposition be the same as the SVD, and when (for instance the first matrix of homework 7 question 4 has the same eigen-decomposition and SVD I think)?

  • HW6: Q6, Q7.1, Q7.3.

Today

  • MV calculus and optimization (cont’d).