hilbert space - How do you subtract colors and divide them by irrational numbers? (Gluons)

There is a gluon that is

$$\frac{1}{\sqrt{3}} (red \cdot\overline{red} + blue\cdot\overline{blue} - 2\cdot green \cdot\overline{green})$$ This confuses me because I do not understand how adding and subtracting and dividing these colors would work. I know that in matrix form it is $$A = \frac{1}{\sqrt{3}} \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -2 \end{pmatrix}$$ This still confuses me, please help me. This is the 8th Gell-Mann matrix.