Yoshio Mikami

On the Japanese Theory of Determinants

It is very remarkable that the theory of determinants had developed in Japan independent of, and even preceding, the progress in the West. The subject was considered some years ago by Prof. T. HAYASHI (1), who was the first historian of mathematics to take notice of it (2). In my Development of Mathematics in China and Japan, Leipzig, 1913, p. 191-199, 1 also mentioned something of the matter. But it will not be without interest to try a further account in the following lines. The oldest of the documents concerning the subject before us is doubtless the Fukudai of SEKI K6WA, which bears the date of 1683. In this manuscript and in all other treatises which we have examined the Japanese theory of determinants was invariably applied to the elimination of an arbitrary quantity between two equations containing it. This is a feature that is most interesting, and that must not be overlooked. It will be sufficient to treat only of the case where the two equations are of the same degree, and let them be given in the form