Sign-Solvable Cone-Systems
Si-Ju Kim, Bryan L. Shader · Linear and Multilinear Algebra · 2002
Qualitative properties shared by the solutions to the family of linear equations of the form $$Ax=b, \quad (A\in C, b \in B),\eqno(1)$$ where C is a cone in ${\shadR}^{m\times n}$ and B is a cone in ${\shadR}^m$ are studied. In particular, the cones C and B for which the sign patterns of the solutions to (1) are independent of the choice of A ε C and b ε B are characterized.