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gibson:teaching:fall-2014:iam961:iam-961-hw2

# IAM 961 HW2

Use Matlab to demonstrate how uniqueness works for complex matrices, along the lines of the SVD demo in lecture. Specifically

Case 1: Distinct singular values

1. Create a random 4 x 4 complex matrix with distinct singular values and known SVD 2. Compute the SVD of .
3. Of the two SVDs, what should be the same? What is likely to be different?
4. Show that the third column of is “colinear” with the third column of , where the constant of linearity is a complex number with unit magnitude.
5. Do the same for the third columns of and . What is the relation between this constant and the constant of the previous question?

Case 2: Repeated singular values

1. Create a random 4 x 4 complex matrix with and known SVD 2. Compute the SVD of .
3. Of the two SVDs, what should be the same? What is likely to be different?
4. Show that the first two columns of span the same 2d subspace as the first two columns of (do this by showing that the first two columns of are in the span of the first two columns of , and vice versa).

Keep a diary of your work in Matlab (diary on). Edit the diary text file to remove mistakes and extraneous material, and turn in a printout of the text file. Use comments to explain what you are doing, in the style of the SVD demo 