# HW4 - COT4501 Spring 2012 Homework IV This assignment has...

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COT4501 Spring 2012 Homework IV This assignment has seven problems. The assignment is due in class on Thursday, March 1, 2012. There are five regular problems and two computer problems (using MATLAB). For written problems, you need to show your work and it is insufficient to just give the results or answers. For the computer problems, turn in your results (e.g., graphs, plots, simple analysis and so on) and also a printout of your (MATLAB) code. Problem 1 (15pts) 1. True or false: All the eigenvalues of a real matrix are necessarily real? 2. True or false: The condition number of a matrix with respect to solving linear systems also determines the conditioning of its eigenvalues. 3. For a given matrix A : Can the same eigenvalue correspond to two different (non-multiple) eigenvectors? Can the same eigenvector correspond to two different eigenvalues? 4. Which of the following conditions necessarily imply that an n × n real matrix A is diagonalizable (i.e., is similar to a diagonal matrix)?

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