How do i write a code which can calculate the null space basis of two random matrix?

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How do i write a code which can calculate the null space basis of two random matrix?
a=randn(5,3)
b=randn(5,3)
c=null([a;b])
The window always show me
Empty matrix: 5-by-0
Or is there any condition of matrix before we use the null command?
  4 Comments
John D'Errico
John D'Errico on 24 Sep 2019
If the combined matrices are full rank when you combine them, the null space is empty. The probability is 1 that any random parir of matrices has full rank as you have built them.
Therfore that you got an empty result is TOTALLY expected. In fact, I would be immensely surprised if two such random 5x3 matrices, then combined into a 5x6 matrix did not have a rank of 5.
yang-En Hsiao
yang-En Hsiao on 24 Sep 2019
but you can find the null space by svd,why can't i use the null command to find the null space

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Answers (1)

Matt J
Matt J on 24 Sep 2019
Edited: Matt J on 24 Sep 2019
This is the result the code you posted produces,
c =
3×0 empty double matrix
The matrix [a;b] has full column rank,
>> rank([a;b])
ans =
3
and so has no non-trivial null vectors. Plain and simple.
  2 Comments
yang-En Hsiao
yang-En Hsiao on 24 Sep 2019
but you can find the null space by svd,why can't i use the null command to find the null space
Matt J
Matt J on 24 Sep 2019
You can, and you have. The output of null is telling you that [0;0;0] is the only null vector.

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