SUMMARYThis paper is concerned with the development of a 'best' rank one transitive approximation to a general paired comparison matrix in a least-squares sense. A direct attack on the non-linear problem is frequently replaced by a sub-optimal linear problem and, here, the best procedure of this kind is obtained. The Newton-Kantorovich method for the solution of the non-linear problem is also studied, including the role of the best linear approximation as a starting point for this method. Numerical examples are included.

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Properties of the right eigenvectors associated with the conjugate pairs of complex eigenvalues of H‐selfadjoint matrices are investigated. Making use of the solution of certain matrix equations, explicit formulae are obtained expressing the connection between the complete sets of right Jordan chains corresponding to the complex conjugate eigenvalues.

Abstract-Highly forsteritic olivine (Fo: 99.2-99.7) in the Kaba meteorite emits bright cathodoluminescence (CL). CL spectra of red luminescent forsterite grains have two broad emission bands at approximately 630 nm (impurity center of divalent Mn ions) in the red region and above 700 nm (trivalent Cr ions) in the red-IR region. The cores of the grains show CL blue luminescence giving a characteristic broad band emission at 400 nm, also associated with minor red emissions related to Mn and Cr ions. CL color variation of Kaba forsterite is attributed to structural defects. Electron probe microanalyzer (EPMA) analysis shows concentrations of Ca, Al, and Ti in the center of the forsterite grain. The migration of diffusible ions of Mn, Cr, and Fe to the rim of the Kaba meteoritic forsterite was controlled by the hydrothermal alteration at relatively low temperature (estimated at about 250°C), while Ca and Al ions might still lie in the core. A very unusual phase of FeO (w€ ustite) was also observed, which may be a terrestrial alteration product of FeNi-metal.