What is the difference between null(A) and null(A,'r') in Matlab ?

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What is the difference between null(A) and null(A,'r') in Matlab ? Could you give me an example ? thanks

Accepted Answer

Wayne King
Wayne King on 4 Jan 2014
Edited: Wayne King on 4 Jan 2014
null(A,'r') does not give an orthonormal basis for the nullspace of A.
The help has a good example of this.
Orthonormal basis for nullspace of A
A = [
1 2 3
1 2 3
1 2 3];
Z = null(A);
norm(Z(:,1),2)
norm(Z(:,2),2)
Next try:
Zr = null(A,'r');
Note the above columns are not orthonormal, but
A*Zr
yields the zero matrix. So clearly both columns of Zr are elements of the nullspace of A. Note that the columns of Zr are linearly independent
rank(Zr)

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