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Published online by Cambridge University Press: 20 January 2009
In this note we wish to study some properties of a square matrix of order n and of rank r,
whose coaxial minors |M| of certain orders, or some of them, are known to be zero. Our main results will lie in two directions, according as the vanishing minors are, within certain limits, of an arbitrary order (Part II) or of two consecutive orders only (Part III).
page 210 note 1 This is at most one half and generally a much smaller fraction of the number nCm of all coaxial minors of the same order.
page 210 note 2 In the case n = 3, one more form appears.
page 211 note 1 Gött. Nachrichten (1899), 272–281Google Scholar.
page 211 note 2 Kantor, , loc. cit., Frobenius, Journal fur Math., 82 (1877), 230–315,Google Scholar and Sitzb. der Preuss. Akad. Wiss. (1894), 241–256.Google Scholar
page 211 note 3 Amer. Math. Monthly, XLI (1934), 607–608.Google Scholar
page 211 note 4 These are, for n > 3, contained in 1.3.
page 216 note 1 Kronecker, , Journal für Math., 72 (1870), 152–175.Google Scholar
page 216 note 2 loc cit., p.
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