Is there a function out there to find a matrix parameter so that the Eigenvalues come out to be a predetermined number?

So, what I basically need is some variation of the solve function so that, given the following matrix (the real matrix I'm using is 7x7):

M =[(1-theta), 0, -theta*alpha, theta*alpha0;
    -theta*alpha, (1-theta), 0, theta*alpha0;
    0, -theta*alpha, (1-theta), theta*alpha0;
    0, 0, 0, 1];

I can screen values of, say, alpha, to find at least one so that the dominant Eigenvalue is 1 (I'm looking for an oscillating system).

Now, one of the biggest problems I've come across is that I cant simply use the

max(eig(M))

function because I already have a value = 1 (given the last row) which is meaningless. Not only that, I have to remove the imaginary part of the Eigenvalues (I don't care about the frequency of oscillation).

Thank you so much for the help!

German

Answer 1

[Youssef Khmou]

hi, try :

 max(abs(eig(M)));

[German Sabio]

Thanks, Youssef, but this doesn't help me. It only partially solves the problem: It takes away the imaginary part of the numbers, yes, but I still have the problem of evaluating the "second highest" number in an auntomatic way......... :(

[Youssef Khmou]

i think the values are sorted no? ok try to use the function sort :

 M=rand(10);
 L=sort(abs(eig(M)),'descend');
 N=L(2); % second highest number 

 % or without the || operator
 %N2=sort(eig(M),'descend');

Answer 2

[Alan Weiss]

FYI, there is a documentation example that is similar to the answer that Youssef gave.

Alan Weiss

MATLAB mathematical toolbox documentation