Compact Notation of RxN Mechanism

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SUMMARY

The discussion centers on the interpretation of coefficient matrices {{\nu'_{ji}}} and {{\nu''_{ji}}} in a combustion text, specifically regarding their proper mathematical classification. The user questions whether these matrices can be multiplied by a vector to yield the system of equations presented in equation 4.29. Additionally, there is confusion over the reversed indices (i.e., i as the row index and j as the column index), which deviates from standard matrix notation conventions.

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  • Research the properties of coefficient matrices in chemical kinetics
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Students and professionals in chemical engineering, particularly those focusing on combustion processes, as well as mathematicians and physicists dealing with matrix operations in scientific contexts.

Saladsamurai
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Hello all!

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

Doc-8_27_109_17PM-page-1.jpg


Am I correct in saying that the "coefficient matrices" {[itex]{\nu'_{ji}}[/itex]} and {[itex]{\nu''_{ji}}[/itex]} 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!
 
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Hmmm ... maybe I am Wrong here and I AM just tired:

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

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

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