how do i find a set using matrix

i have a matrix and also lower and upper bound for it.

firstly the set is empty and i want to inclue the matrix element a11 in a set. then reduces matrix using the following command,

Q(Q(1,:)==1,:)=[]
>> Q(:,Q(1,:)==1) = []
>> Q(:,1)=[];
>> Q(1,:)=[];

after that again add a11 element in a set..so i have a set...and this process done untill the matrix is null.

Answer 1

[DGM]

Like this?

sza = 10;
A = randi([1 10],sza)

A = 10×10

3 6 2 5 5 8 8 4 9 8 4 1 8 6 8 5 10 9 9 9 7 7 1 10 4 6 2 10 3 8 1 3 9 9 10 10 8 4 3 9 1 4 4 5 9 9 7 1 2 5 10 3 3 2 8 8 4 10 2 10 6 4 1 3 7 4 6 3 4 3 1 3 3 9 4 3 1 2 9 8 5 7 9 9 3 3 7 3 6 6 1 10 5 9 10 6 7 5 2 7

% output will be variable-length
% preallocate to maximum length
kmax = max(size(A,1),size(A,2));
outvec = zeros(1,kmax);

k = 0;
while ~isempty(A)
	outvec(k+1) = A(1,1);
	k = k+1;
	
	A(A(1,:)==1,:) = [];
	if isempty(A); break; end
	A(:,A(1,:)==1) = [];
	
	% it's not clear if these cases should still be used
	% if the first row/column has already been deleted in the prior lines
	if isempty(A); break; end	
	A(:,1) = [];
	if isempty(A); break; end
	A(1,:) = [];
end

% crop off excess vector length
outvec = outvec(1:k)

outvec = 1×8

3 1 9 9 8 6 6 7

That might simplify, but it still seems too ambiguous to bother optimizing.

[Kajal Agrawal]

thankyou for your responce..i have tried this but didn't get my actual set.

for example, suppose that the matrix is,Q=[4 1 1 0 1 1; 1 4 0 1 1 1; 1 0 4 1 1 1;0 1 1 4 1 1;1 1 1 1 4 0; 1 1 1 1 0 4].

then we include A11 element in a set S then set S={1}, then we reduced the matrix,

Q(Q(1,:)==1,:)=[];

>> Q(:,Q(1,:)==1) = [];

>> Q(:,1)=[];

>> Q(1,:)=[];

after that the matrix will be, Q=[4] then add this element in a set. so the set will be S={2}.again continue ths steps ,we get null matrix and set S={2}.

thankyou.

[DGM]

If Q is:

Q=[4 1 1 0 1 1;
   1 4 0 1 1 1; 
   1 0 4 1 1 1;
   0 1 1 4 1 1;
   1 1 1 1 4 0;
   1 1 1 1 0 4]

Q = 6×6

4 1 1 0 1 1 1 4 0 1 1 1 1 0 4 1 1 1 0 1 1 4 1 1 1 1 1 1 4 0 1 1 1 1 0 4

Then what is A11? I assume you meant Q(1,1), because there's otherwise no other mention of an array called A or a variable called A11. If you meant Q(1,1), then why is S set to 1?

As you say, after doing those operations, Q has been reduced to a scalar 4. If this element (4) is added to the set, then why is S = 2?

Q(Q(1,:)==1,:)=[];
Q(:,Q(1,:)==1) = [];
Q(:,1)=[];
Q(1,:)=[];

Q

Q = 4

Something is missing from this explanation.

[Kajal Agrawal]

Yes you are right, perhaps i'm not able to gives you a proper explain, Q(1,1)=4 and i want to counting this element in a set.