Return submatrix that has Full Rank

So I have P = ctrb(A,C) which returns the controllability matrix. which is say 5x10 Now if it has full rank, I want MATLAB to just return the 5x5 matrix that fulfills the rank requirement. How can I do this? Because I need to use that P matrix in further calculations but I can't do it with the 5x10 matrix that MATLAB gives me, I need the 5x5

[KSSV]

Keep taking five columns randomly and check the rank.

Answer 1

[David Goodmanson]

Hello Shubham,

% make up an example
nrow = 5;
ncol = 10;                 % ncol > nrow
A = rand(nrow,ncol);
A = [A(:,1),A(:,2),A];   % toss in some duplicate columns to make sure they get rejected 

At = A';                 % work with transpose
[m n] = size(At);        % m > n
[~, ~, p] = lu(At);
Atsub = p*At;
Asub = Atsub(1:n,:)';     % take top rows, transpose back
ind = p*(1:m)';
ind = ind(1:n)';         % index shows which columns were selected 
format compact
Asub
A                        % visual check that all columns of Asub are contained in A
ind
rank(Asub)