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Find which variables must be zero for non-negative solution to homogeneous linear equations
Some addition to @Alexey answer.
There are many good solvers for LP (linear programming) problems; and if you are only dealing with some thousands of variables, open source solvers will suffice. ...
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Find which variables must be zero for non-negative solution to homogeneous linear equations
If you are interested In an algorithmic solution I suggest the use of linear optimization.
For example, say we have a system of equations:
$$A\cdot x = 0$$
and we wish to check if $x_i$ always ...
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Find which variables must be zero for non-negative solution to homogeneous linear equations
A simple approach is to use linear programming (LP). For each $j$, the problem is to maximize $x_j$ subject to $Ax=0$ and $x \ge 0$. For your example matrix $A$, the optimal objective value is $0$ ...
- 34k
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