Homework assignments #

Below are the homework assignments for each week. Problem numbers refer to the appropriate sections of this website.

You should watch the following short videos on the singular value decomposition; take notes and be an active participant as you do. Pause, and try to answer questions as they arise.

• Matrix diagonalization, a quick review
• The SVD
• Computing the SVD
• Geometry of the SVD
• Eigenvalues vs. singular values

Use the technique developed in the lectures to compute the SVD for the following matrices:

\[ \begin{pmatrix} 3 & 0\\ 0 & -2 \end{pmatrix} \;\;\; \begin{pmatrix} 2 & 0\\ 0 & 3 \end{pmatrix} \;\;\; \begin{pmatrix} 1 & 1\\ 0 & 0 \end{pmatrix} \;\;\; \begin{pmatrix} 1 & 1\\ 1 & 1 \end{pmatrix} \]