Translation matrix

Figure 10. A stereodiagram showing a comparison of the active site geometry of Streptomyces griseus protease A (SGPA) with that of bovine -trypsin. SGPA is presented by solid bonds, trypsin by open bonds. The root mean square deviation after minimisation by application of an appropriate rotation translation matrix is 0.39 A for some 62 common atom positions. From [97].

Incommensurism At least one of the elements p,q,r, and s is irrational and neither column of the translation matrix consists of integers. Under this condition, no distinctive registry between the substrate lattice and the deposit lattice exists. 

Considering a translation-translation matrix element M, , we note that translational displacements u, are antisymmetric to inversion. As a result, we obtain... 

Standard deviation r indicates the type of quantity (n.d.) Translation matrix (-)... 

By inspection of (9.13.39), we see that the translation matrix W is a lower triangular matrix with unit diagonal elements. This structure implies that the monopole moment at P makes contributions to all multipoles at P, that the dipole moment at P makes contributions to the dipole and all higher moments at P, and so on. In particular, we note that a charge distribution that is represented exactly by a finite number of multipoles centred at P, will require an infinite expansion at a different position P for an exact evaluation. 

Obviously, this matrix representation has the same form as in the complex case, with identical summation ranges. Since the real multipole moments and translation-matrix elements have one instead of two components as in the complex counterpart to (9.13.66), the real formulation is more compact. 

Let us finally consider the real expression for the interaction matrix. We proceed in the same maimer as for the translation matrix, beginning with (9.13.19), which we write as... 

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