Find random samples of some rows in the matrix and ensure the rank

I have a matrix 'A':

A = [ 1.2285      -1.2285   2.3433e-17  -4.1658e-17
      0.70827     -0.70827    1.351e-17  -2.4017e-17
      -1.2285       1.2285  -4.1658e-17   5.9885e-17
  -1.8226e-17   4.1658e-17       1.0932      -1.1271
  -2.4017e-17   2.4017e-17      0.63025     -0.64979
  -4.1658e-17   4.1658e-17       -1.161       1.1948
            0            0       1.1159            0
            0            0            0       1.0901];

I want to find the random sample of some rows 'index' in matrix 'A' so that each sample A(index,:) ensure rank.

Answer 1

[Matt J]

What does it mean to "ensure the rank"? Do you mean you want to find a random full-rank subset of rows? If so,

A = [ 1.2285      -1.2285   2.3433e-17  -4.1658e-17
      0.70827     -0.70827    1.351e-17  -2.4017e-17
      -1.2285       1.2285  -4.1658e-17   5.9885e-17
  -1.8226e-17   4.1658e-17       1.0932      -1.1271
  -2.4017e-17   2.4017e-17      0.63025     -0.64979
  -4.1658e-17   4.1658e-17       -1.161       1.1948
            0            0       1.1159            0
            0            0            0       1.0901];


M=size(A,1);
N=rank(A);

B=[];
while rank(B)<N
 
    index=randperm(M,N);
    
    B=A(index,:);
    
end

index=sort(index), 

index = 1×3

3 5 8

B=A(index,:)

B = 3×4

-1.2285 1.2285 -0.0000 0.0000 -0.0000 0.0000 0.6302 -0.6498 0 0 0 1.0901

[NA]

Do you mean you want to find a random full-rank subset of rows?

I mean, a heuristic search to avoid non-observable set.