How to write this matrix in matlab, - matlab

Question

I want to write this matrix in matlab,
s=[0 ..... 0
B 0 .... 0
AB B .... 0
. . .
. . .
. . . 0 ....
A^(n-1)*B ... AB B ]
I have tried this below code but giving error,
N = 50;
A=[2 3;4 1];
B=[3 ;2];
[nx,ny] = size(A);
s(nx,ny,N) = 0;
for n=1:1:N
s(:,:,n)=A.^n;
end
s_x=cat(3, eye(size(A)) ,s);
for ii=1:1:N-1
su(:,:,ii)=(A.^ii).*B ;
end
z= zeros(1,60,1);
su1 = [z;su] ;
s_u=repmat(su1,N);
seems like the concatenation of matrix is not being done.
I am a beginner so having serious troubles,please help.

Answer 1

Use cell arrays and the answer to your previous question
A = [2 3; 4 1];
B = [3 ;2 ];
N = 60;
[cs{1:(N+1),1:N}] = deal( zeros(size(B)) ); %// allocate space, setting top triangle to zero
%// work on diagonals
x = B;
for ii=2:(N+1)
[cs{ii:(N+2):((N+1)*(N+2-ii))}] = deal(x); %//deal to diagonal
x = A*x;
end
s = cell2mat(cs); %// convert cells to a single matrix
For more information you can read about deal and cell2mat.
Important note about the difference between matrix operations and element-wise operations
In your question (and in your previous one) you confuse between matrix power: A^2 and element-wise operation A.^2:
matrix power A^2 = [16 9;12 13] is the matrix product of A*A
element-wise power A.^2 takes each element separately and computes its square: A.^2 = [4 9; 16 1]
In yor question you ask about matrix product A*b, but the code you write is A.*b which is an element-by-element product. This gives you an error since the size of A and the size of b are not the same.

Answer 2

I often find that Matlab gives itself to a coding approach of "write what it says in the equation". That also leads to code that is easy to read...
A = [2 3; 4 1];
B = [3; 2];
Q = 4;
%// don't need to...
s = [];
%// ...but better to pre-allocate s for performance
s = zeros((Q+1)*2, Q);
X = B;
for m = 2:Q+1
for n = m:Q+1
s(n*2+(-1:0), n-m+1) = X;
end
X = A * X;
end