Nontrivial diagonal matrix

Of course, if each gas lives separately in the reactor and all matrices, especially Ks(5), are diagonal, the comprehensive matrix with all gases will not offer new information. The nontrivial cases occur when adsorbed gases transform from one species to another, so that Kss holds the kinetic information of the surface reaction system and Ks(s) is no longer diagonal. 

A nontrivial solution (not all Cj = 0) requires that the determinant of H - E, where E is the diagonal eigenvalue matrix, is equal to zero. Evaluation of this matrix gives a polynomial P(E). The secular equation P(E) = 0 gives the eigenvalues and guarantees a nontrivial solution. The eigenvalues Ej satisfy the secular equation. 

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