Matrix inner matrix matlab

Question

I try to input matrix in matrix

A=[1 2;2 1];
C=[0 1];

and then input the matrix in new matrix with

D =[CA;CA^2;CA^3;........;CA^n]

i try to use

n=40;

a(1,1)=1;
a(1,2)=1;
a(2,1)=1;
a(2,2)=1;
C=[0,1];



for k=1:n
   for i=1:2
      for j=1:2
          d(i,j)=c*a(i,j)*^n
      end
   end
end

when n is integer but i can't do

how to solve it ?

thank you very much for your attention

@Okuma.Scott maybe the question is ill-posed but there are some obvious misunderstandings of the basics of MATLAB syntax that need to be addressed. — Falimond, Nov 25 '13 at 17:49
@Falimond Sorry, I guess I'm becoming jaded. Good answer BTW. — Scott Solmer, Nov 25 '13 at 18:02
@Falimond BTW it is best [not to use `i` and `j` as variable names in Matlab](http://stackoverflow.com/questions/14790740/using-i-and-j-as-variables-in-matlab). — Shai, Nov 26 '13 at 11:36
@Shai Thanks for the suggestion. I've realized it in the past but rarely deal with complex quantities so it's become a bad habit. — Falimond, Nov 26 '13 at 18:51

Falimond · Answer 1 · 2013-12-07T08:43:06.460

First off, there is no need to declare the elements of A individually. As you show it in your first code snippet is fine.

So the main issue with this for loop (besides the fact that it doesn't actually mimic the process shown here D =[CA;CA^2;CA^3;........;CA^n]) is that you are using the variable n in d(i,j)=c*a(i,j)*^n when in fact it is the variable k that is being incremented by the first for loop. So you are always computing d(i,j)=c*a(i,j)*^40 and should instead use k in pace of n.

a(i,j)*^k is also incorrect syntax since *^ does not multiply nor does it exponentiate. MATLAB will return an error because of this.

Additionally, you will get Subscripted assignment dimension mismatch. error because C is 1x2 matrix and A(i,j) is just one element.

The reason I said it won't mimic the process D =[CA;CA^2;CA^3;........;CA^n] is because you are only doing element wise operations on C with A and then putting them into D, I'm fairly certain this is not your run of the mill matrix multiplication - even if you were to break it down correctly - but this is inefficient since MATLAB will do it for you.

clear D
n=10;

A=[1 2;2 1];
C=[0,1];

for k=1:n
    D(k,:) = C*A^k;
end


D =

       2           1
       4           5
      14          13
      40          41
     122         121
     364         365
    1094        1093
    3280        3281
    9842        9841
   29524       29525

score 2 · Answer 2 · edited May 23 '17 at 11:59

Great answer by Falimond.
However, significant number of matrix multiplications can be saved here:
Instead of taking A to the power of k for each k, we only need to multiply by A the result of the previous iteration: D(k,:) = C*A^k = D(k-1,:)*A!

n = 10;
A = [1 2;2 1];
C = [0 1];
D = zeros(n, size(C,2) ); % pre-allocate always a good practice
D(1,:) = C*A; % init recursive process
for k=2:n
    D(k,:) = D(k-1,:)*A;
end

Matrix inner matrix matlab

2 Answers2