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ps7[1] - Applied Mathematics E2101y Introduction to Applied...

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Applied Mathematics E2101y Introduction to Applied Mathematics Problem Set #7, due Thursday, 9 April 2009 All references are to Zill & Cullen (3rd edition). Chapter 8, § 8.8: The Linear Eigenvalue Problem 5 12 23 27 [You do not need to submit the logs of any computer experiments, but you are welcome to perform those indicated on your own in order to arrive at a conjecture about the leading eigenvalue and its associated eigenvector for matrices whose row sum is one and all of whose elements are nonnegative. You should submit your conjecture, and show why it is true with a simple matrix-vector multiplication, a one-line proof.] Chapter 8, § 8.9: Powers of Matrices 1 7 15 Chapter 8, § 8.10: Orthogonal Matrices 2 15 Chapter 8, § 8.11: Eigenvalue Approximation
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