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eliminate the nullspace of a matrix

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Ano
Ano on 7 Aug 2017
Commented: Zoltán Csáti on 20 Aug 2018
Hello, how can I eliminate the nullspace of a square matrix using Matlab? Thank you!

  2 Comments

John D'Errico
John D'Errico on 7 Aug 2017
Sorry, but eliminating the nullspace of a matrix has no meaning, just some jargon that you have made up. Define carefully what you want to do. Only you know that.
A matrix has a nullspace. That null space may be empty or not. But you cannot "eliminate" it. So what do you want to do?
Torsten
Torsten on 7 Aug 2017
If you want a basis of the row space of A, use orth(A.').
The rule is that
null(A) + orth(A.') = R^n
where n is the dimension of your matrix.
Best wishes
Torsten.

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Accepted Answer

Azzi Abdelmalek
Azzi Abdelmalek on 7 Aug 2017
If you have any matrix, square or not, you have only one possibility: remove entire rows or columns that are equal to zero
Example
A=[1 2 3 0;0 0 0 0;1 4 5 0 ;2 7 8 0]
ix=~any(A,1)
A(:,ix)=[]
iy=~any(A,2)
A(iy,:)=[]

  1 Comment

Zoltán Csáti
Zoltán Csáti on 20 Aug 2018
Non-empty null space is possible without having zero rows/columns.

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