Homogenous Equation System
# Definition
Let $V, W$ be Vector Spaces over the same Field $F$. Let ${f_{\alpha}\in W^{V}}{\alpha \in A}$ and ${b{\alpha} \in W}{\alpha \in A}$ define an Equation System $$f{\alpha}(x)= b_{\alpha} \text{ }\forall \alpha \in A$$ for some Index Set $A$. This Equation System is a Homogenous Equation System if the Solution Set is a Vector Subspace of $V$.