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

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NA 2021-4-30

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/818485-find-random-samples-of-some-rows-in-the-matrix-and-ensure-the-rank

编辑： NA 2021-5-2

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.

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Answer 1

Matt J 2021-5-1

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https://ww2.mathworks.cn/matlabcentral/answers/818485-find-random-samples-of-some-rows-in-the-matrix-and-ensure-the-rank#answer_689290

编辑：Matt J 2021-5-1

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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