How to get the minimum number of rows that, if removed, reduces the rank.

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I have a matrix A
How can I get the number of rows that make matrix A rank deficient.
for example
A =[ 6.5480 -6.5480 0.0000 -0.0000
6.5480 -6.5480 0.0000 -0.0000
-6.5480 6.5480 -0.0000 0.0000
-0.0000 0.0000 5.8267 -6.0073
-0.0000 0.0000 5.8267 -6.0073
-0.0000 0.0000 -6.1879 6.3685
0 0 1.0000 0
0 0 0 1.0000]
rank_A =rank(A)
The rank of A is 3, if I remove 3 rows, the rank of the matrix changes to 2.
So, the result should be 3 ---> number of rows

Risposte (1)

Matt J
Matt J il 28 Giu 2020
Well, if A were full rank, it's rank would be
min(size(A));
So, perhaps you want the difference between this and the actual rank.
  13 Commenti
NA
NA il 23 Apr 2021
If A is
A =[ 6.5480 -6.5480
6.5480 -6.5480
-6.5480 6.5480];
subsets are
subset{:}
ans = 6.5480 -6.5480
ans = 6.5480 -6.5480
ans =-6.5480 6.5480
So numel(subset) is 3,
optimal_numbe_of_removed_rows>=3
I think it should be
Nopt>=size(subset{1},1)
Matt J
Matt J il 23 Apr 2021
Modificato: Matt J il 23 Apr 2021
optimal_numbe_of_removed_rows>=3
That's correct. Because rank(A)=1 in your example, the only way to reduce the rank is to remove all 3 rows.

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