TITLE:
Hermitian Symmetry on a Hilbert Space—Its Applications to Some Asymmetric Phenomena
AUTHORS:
Naohito Chino
KEYWORDS:
Hermitian Symmetry, Hilbert Space, Asymmetric Similarity, Asymmetric MDS
JOURNAL NAME:
Natural Science,
Vol.12 No.5,
April
29,
2020
ABSTRACT: 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.