I think I did this question completely incorrectly.

Power Iteration on Generalized Eigenvalue Problems mints Consider now the problem of nding eigenvalues of a generalized eigenvalue problem: nd scalar A and nonzero vector 3: 6 IR\" such that Am : AMI, where A, M 6 RM" are both nonsingular matrices, M is an upper triangular matrix. 1. What non-generalized (standard) eigenvalue problem is the problem equivalent to? 2. Outline the normalized power iteration procedure for the generalized eigenvalue problem. Can the power iteration be done without explicitly forming the standard eigenvalue problem? It N power iterations are performed where N is much smaller than n, how many operations are necessary? (You should give an expression in terms of N and n.) 3. Suppose we know that one eigenvalue is close to pi and want to calculate this eigenvalue. Describe an algorithm to calculate this eigenvalue using the inverse iteration with shift. How many operations are necessary if N power iterations are performed where N is much smaller than n? (When oounting the operations, you only need to give the asymptotic bound. For example, if the number of operations is 3115 + 10Nn4 + 241113, showing 0(115 + N124) would be enough.)