For a final project in my linear algebra intro, I have been tasked with writing a script that finds the largest and the second largest eigenvectors of a symmetric matrix in Matlab. For the best possible grade, it must include a function as well. So far, I have been able to get my script to verify that a matrix is symmetric, and am feeling a little bit stuck. I need some guidance for finishing this assignment, as my Matlab experience is extremely limited.
Here is what I have so far:
prompt = 'Please input a symmetric matrix A.' A = input(prompt); if (A == A'), eig(A) else disp('A is not a symmetric matrix. Please input a symmetric matrix.') end
Note that the script hopefully verifies that
A is symmetric, and I have the eigenvalues for
A, but I am not sure where to go from here to $1$. find the eigenvectors, $2$. get the two largest eigenvectors, and $3$. write a useful function to fit into the script. I would be very grateful for any help given. Thanks!