Solving A x = 0 for non-negative x The problem is simple. I have a large matrix and w

Yesenia Obrien

Yesenia Obrien

Answered question

2022-07-09

Solving A x = 0 for non-negative x
The problem is simple. I have a large matrix and would like to find a vector in its nullspace such that the components are greater than equal to zero, i.e., solve:
A x = 0  subject to:  x i 0
It is possible to find a basis for the nullspace of A numerically, but this just leads to a system of linear inequalities which I am unsure how to solve:
B c 0
where the columns of B are the nullspace basis vectors. If I can solve this for c then the solution to the previous problem is just x = B c.

Answer & Explanation

lofoptiformfp

lofoptiformfp

Beginner2022-07-10Added 16 answers

You can solve this as a linear programming problem, e.g.:
maximize i x i
subject to A x = 0
all 0 x i 1
The upper bounds are to make the problem bounded.

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