creating loop and storing eigenvalues from random matrices

Hi,

I am very new to Matlab and I am currently trying to write a code on Matlab for a specific task. I believe I need to write a loop.

I want to generate a 2x2 random covariance matrix so the diagonal entries are in the interval [0,1] and the non-diagonal entries are in the interval [-1,1]. I would like to compute the eigenvalues of this matrix which is straight forward.

Here is the difficult part: But I want to repeat this process for many (say 100 times) random 2x2 covariance matrices. Then for each matrix, I get 2 eigenvalues. I want to be able to store the eigenvalues for all 100 matrices into one vector, giving me a 2*100 = 200-entry vector.

I suspect my code will contain something of the following:

a=-1+2*rand;
A=[rand a; a rand];
v=eig(A)

I am just unsure on how to create a loop with allows me to repeat this task for say 100 times and to store the entries as a big vector.

Answer 1

[Walter Roberson]

many_times = 100;
all_v = zeros(2, many_times);
for K = 1 : many_times 
  a = -1+2*rand;
  A = [rand a; a rand];
  v = eig(A);
  all_v(:, K) = v;
end

[Vivi]

Hi Walter, Thanks for the fast reply. I think this is nearly correct. Here I have a 2x100 vector. I would like 1x200 vector. So say for the first eigenvector, the 1st and 2nd entries of all_v is just eigenvalues of the first eigenvector. And the 3rd and 4th entries of all_v are the eigenvalues of the second eigenvector.

I basically want to plot a histogram of these eigenvalues and get an eigenvalue spectra.

[Vivi]

Ooh, I discovered the reshape function, that did the trick! Thank you Walter, much appreciated!