## Lecture 21: SVDs (continued)

Some scribe notes for the lecture are up on the web page. They incorporate two bug fixes, and the proof that the least-squares solution to ${\| Ax - b \|}$ is indeed ${x = A^+ b}$, which we did not do in lecture.

The bug fixes, so you know where to look: I said something about the behavior of ${A^+}$ on the vectors in the kernel of ${A}$, that entire sentence did not make any sense, just ignore it. Also, in the distinct singular values case, the singular vectors are unique only up to sign (duh!), and they’d better be sorted in decreasing order for uniqueness to hold. The notes incorporate those fixes.

The HW will be out by tomorrow, due on Friday the 20th.