A)

Create a matlab function that employs the Power Method (PM) to find the largest eigen value(evalue) and eigen vector (evector) of a matrix X. The prototype of the function should look like the following.

function [evalue, evector] = PM_eigen( X )

Be sure to check that the matrix is square and to limit the number of iterations to some large count (1000). Use some method to indicate to the calling function that no solution was found(evalue = NaN)?

B)

Once we have an eigenvalue and vector, we will want to remove that eigenvalue - vector set from the matrix. This removal (or deflation) can be done by the following equation

Lambda is the eigen value and v is the eigen vector

Create a function that will remove an eigenvalue vector set from a matrix returning a matrix. function [Xreduced] = Eigen_Deflate( X, eigenValue, eigenVector );

C)

Employ these two functions to search for all the eigenvalue vectors in the matrix X. function [vectors,values] = EigenVV( X ); Note the eigenvectors will be the columns of the return-value vectors, and the eigenvaluesshould be placed in the diagonal elements of return-value values, an N x N matrix, all otherelements are zero.

Reduced X v v