HCR - Theorem 'At Least One Solutions for a Grasp Matrix'

We have that the grasp matrix $\left(\overline{\stackrel{ˉ}{G}}\right)$:$\overrightarrow{W_c}=\overline{\overline{G}}\cdot \overline{\overline{F_c}}$==Will accepts $1$ or infinite solutions if and only if $\rho (G)=\rho (G⋮W_c)$, otherwise it accepts no solutions==. Where:

• $\rho (G)$: rank of matrix $G$
• $\rho (G⋮W_c)$: rank of matrix $[G⋮W_c]$
• $\rho (G)=\rho (G⋮W_c)$ means that $G$ has to have maximum rank.