Compact Notation of RxN Mechanism

[Saladsamurai]

Hello all!

I am reading through a combustion text and I am a little flustered by this notation:

Am I correct in saying that the "coefficient matrices" {${\nu'_{ji}}$} and {${\nu''_{ji}}$} are not really "proper" matrices in the sense that there is not a vector that can multiply them that will result in the system of equations given by 4.29? Or is there? And I am just too tired to figure this out?

Also, the fact that the ij indices are reversed from normal convention (i.e., i = row index and j=column index) is really driving me batty!

 

[Saladsamurai]

Hmmm ... maybe I am Wrong here and I AM just tired:

I guess if we multiply $\nu'_{ji}$ by the column vector
$$\left( \begin{array}{c}<br /> X_1\\X_2\\X_3\\X_4\\X_5\\X_6\\X_8<br /> \end{array}\right)$$

The index thing is still bothering me. Usually when we see A_mn we have a matrix in which there are 'm' rows and 'n' columns ...