Hi Efe Berkay,
- To achieve a rank of Hc equal to min (n, k*m), where Hc is the horizontal concatenation of the k binary matrices H₁, H₂, ..., Hₖ, you can modify the generateMatrix function to generate matrices with a desired rank as follows:
function [Y,rk] = generateMatrix(w,y,rank)
P = orth(randi([0 1], w, rank));
Q = orth(randi([0 1], y, rank))';
Y = P*Q;
Y = Y (:, 1:min(size(Y))); % truncate to desired rank
rk = rank(Y);
end
- This modified function generates a binary matrix Y of size w by y with rank equal to the specified rank. Then, it truncates the matrix Y to the first min (w, y, rank) columns, ensuring that the resulting matrix has the desired rank.
- To generate k matrices H₁, H₂, ..., Hₖ with rank equal to m, you can call the modified generateMatrix function in a loop:
n = 10; % size of each matrix
m = 3; % desired rank of each matrix
k = 4; % number of matrices to generate
H = zeros(n, m*k); % initialize H
for i = 1:k
% generate a matrix Hi with rank m
[Hi, ~] = generateMatrix(n, m*k, m);
% add Hi to H
H(:, (i-1)*m+1:i*m) = Hi;
end
% check rank of H
rk = rank(H);
rk_desired = min(n, k*m);
fprintf('Rank of H: %d (desired rank: %d)\n', rk, rk_desired);
- This code generates k binary matrices H₁, H₂, ..., Hₖ with rank equal to m, and concatenates them horizontally to form the matrix H. The rank of H is then checked to ensure that it is equal to the desired rank of min(n, k*m).
Hope it helps!
Regards,
Gayatri Rathod
