Let $\displaystyle R_1=\lambda_{a_1} G_{a_1}+...+\lambda_{a_p} G_{a_p}\ \ , \ \ R_2=\lambda_{b_1} G_{b_1}+...+\lambda_{b_q} G_{b_q},$

where p,q are natural numbers, the lambdas are real constants and the Gs are nxn matrices.

If we have $\displaystyle R_1=R_2$, do we then also have $\displaystyle R_1^T = R_2^T$?