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

Question

Nguyen Trong Nhan 2014-1-4

编辑： Wayne King 2014-1-4

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

Answer 1

Wayne King 2014-1-4

编辑：Wayne King 2014-1-4

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)