General properties of the eigenvalues

If we now choose the eigenvectors Tj such that (So,H ,) = 1, and remember that Sof = I So = 0, then premultiplication of equation (5.5) by Sq yields very simply that 

2 I had thought it advisable to invent another name for this property. Unfortunately, most synonyms for strong possess connotations of determinism, which is entirely inappropriate adjectives like unbiased could be used, but are cumbersome. Quasi-strong is correct, but again cumbersome also, I remember the time when we used the term quasi-unimolecular for the reactions described in this book, so perhaps the qualification quasi- would become redundant here too, before long. 

This much is true, regardless of the nature of the collision matrix. Let us now substitute for R the very simple form for the strong collision relaxation matrix given by 

Finally, substitution of equation (5.9) into equation (5.6) gives us the eigenvalue 

Notice that there are very many zero entries in D corresponding to all the unreactive grains below threshold, and so we have a very large number of eigenvalues of magnitude p. These perturbations are all small and in fact, because the trace of a matrix must equal the sum of its eigenvalues, we find that [79.P3 81.V2] 

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