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

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yang-En Hsiao 2019-9-24

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评论： Matt J 2019-9-24

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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?

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John D'Errico 2019-9-24

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 2019-9-24

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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Matt J 2019-9-24

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编辑：Matt J 2019-9-24

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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.

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yang-En Hsiao 2019-9-24

but you can find the null space by svd,why can't i use the null command to find the null space

Matt J 2019-9-24

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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