Simulating using random orthogonal matrices. How can i create a massive matrix from an equation containing several random matrices and fixed matrices?

I need to create a massive matrix via the eqn: X= Q*L*R*An

where Q and R are random matrices, and L and An are fixed.

I am able to calculate X once, however, what id like to do is the following procedure:

1. Generate Q and R 2. Calculate X 3. Generate new Q and R 4. Calcluate X2 and then merge X2 with X,( to create Xstar) i.e a continuation of X. So that if X=2000*3 and X2= 2000*3 then Xstar=4000*3

Any idea? here som of my code: m=2000 n=3 m and n are matrix dimensions

L=some fixed matrix(2000,3); An=some fixed matrix(3,3);

R=(gallery('randhess',n)); %Upper hessenberg

I=speye(m); % Make Imm Q=I(:,randperm(m));

%Finally compute the equation

X=M*Q*L*R*An;

I suppose i should use a for loop somehow

Any idea? help is much appreciated

Answer 1

[Thorsten]

 for i = 1:N

   M = ...
   Q = ...
   L = ...
   R = ...
   An = ...

   if i == 1
     X = M*Q*L*R*An;
   else
     X = [X ; M*Q*L*R*An]
   end

 end