Abstract
This paper introduces the statistical analyses on the Stiefel manifold and Grassmann manifold, which are treated in the author's book, Chikuse (2003), being written in English. We concentrate our discussion, in particular, on the subjects in the distribution theory for the manifolds. The paper is concerned with the definitions and related topics of the two manifolds, population probability distributions, various decompositions and related distributions, and asymptotic theorems. As for the more detailed discussions and ploofs of the subjects, other statistical analyses, and the theory of invariant polynomials with matrix arguments useful for the derivations, the author advises the reader to refer to the original book of the author.
