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HW4 - 4 Exercise 6.1 Chapter 6 of Trefethen-Bau 5 Consider...

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Math 104 Fall 2009 Homework 4 Due Wednesday, October 28, 2009 1. Exercise 3.5, Chapter 3 of Trefethen-Bau. 2. Let U be an m × m arbitrary unitary matrix. Show that k UA k 2 = k A k 2 and that k UA k F = k A k F . Deduce from this that we also have k AV k 2 = k A k 2 and k AV k F = k A k F , where V is an n × n (arbitrary) unitary matrix. 3. Exercise 5.3, Chapter 5 of Trefethen-Bau.
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Unformatted text preview: 4. Exercise 6.1, Chapter 6 of Trefethen-Bau. 5. Consider the square matrices A and B = A + μI for some scalar μ ∈ C . How do the eigenvalues and eigenvectors of B relate to those of A ? 1...
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