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Hermitian Symmetry on a Hilbert Space—Its Applications to Some Asymmetric Phenomena

The 
purpose of this paper is threefold. One is to revisit the Hermitian form model 
(HFM) with Hermitian symmetry proposed by Chino and Shiraiwa (1993), which 
uncovers the latent Hilbert space structure or the indefinite metric space 
structure, given the asymmetric similarity matrix (ASM) among objects, and 
another is to explain how to interpret the configuration of objects embedded in 
these spaces. The final goal of this paper is to show what kinds of information 
are obtained by applying HFM to empirical and hypothetical ASMs. Results of 
applications of HFM to two empirical ASMs suggest that some possible asymmetric 
structures among objects exist, which might not have been found empirically. The 
result of application of the HFM to a hypothetical ASM uncovers interesting 
latent space structures among objects.