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(in magnitude) eigenvalue of the nonsingular matrix A and the associated
eigenvector x. The input parameter v is an estimate of the eigenvector of A that is
associated with the largest (in magnitude) eigenvalue of A.
25. In this exercise you are to experiment with the eigenvalues and eigenvectors of the
partitioned matrices. Begin with a square matrix A with known eigenvalues and
eigenvectors. Next construct a matrix B using MATLAB's built-in function repmat
to define the matrix B as B = repmat(A, 2, 2). Solve the matrix eigenvalue
problem for the matrix B and compare the eigenvalues and eigenvectors of matrices
A and B. You may wish to continue in this manner using larger values for the second
and third parameters in the function repmat. Based on the results of your experiment,
what conjecture about the eigenvalues and eigenvectors of B can be formulated?
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