Abstract
The implications and applicability of Hermitian from model are discussed for the analysis of asymmetric structure observed frequently in our daily life between objects such as stimuli, persons, regions and nations. The Hermitian form model includes the finite-dimensional complex (f. d. c.) Hilbert space model, the indefinite metric model for asymmetric multidimensional scaling in psychometrics, and the Hermitian canonical model for two-way contingency tables. It is shown that the f. d. c. Hilbert space model is necessary to argue the holistic geometrical structure contained in an observed similarity or dissimilarity matrix, whose elements are composed of the degrees of proximity from object to object. It is also shown that the f. d. c. Hilbert space model has an interesting property. That is, two points in a relatively central region (i. e., near the origin) of the space have a smaller similarity measure than two points of equal interpoint distance but located in a peripheral region (i. e., far from the origin) of the space. It is suggested that we shall sometimes encounter the situation in which the f. d. c. Hilbert space structure is destroyed, and that in such a case the indefinite metric model might serve well. Finally, the possibility of adopting the Hermitian canonical model is suggested in cases where the usual canonical model is not appropriate for the analysis of two-way contingency tables.
