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

2 views (last 30 days)
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

Answers (1)

Matt J
Matt J on 28 Jun 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 Comments
NA
NA on 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 on 23 Apr 2021
Edited: Matt J on 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.

Sign in to comment.

Categories

Find more on Sparse Matrices in Help Center and File Exchange

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!