IV.—Some Factorable Minors of a Compound Determinant
نویسندگان
چکیده
منابع مشابه
On Minors of Maximal Determinant Matrices
By an old result of Cohn (1965), a Hadamard matrix of order n has no proper Hadamard submatrix of order m > n/2. We generalize this result to maximal determinant submatrices of Hadamard matrices, and show that an interval of length ∼ n/2 is excluded from the allowable orders. We make a conjecture regarding a lower bound for sums of squares of minors of maximal determinant matrices, and give evi...
متن کاملOn minors of the compound matrix of a Laplacian
Let L be an n× n matrix with zero row and column sums, n ≥ 3. We obtain a formula for any minor of the (n−2)-th compound of L. An application to counting spanning trees extending a given forest is given.
متن کاملA Simple Derivation of Kronecker's Relation among the Minors of a Symmetric Determinant.
about a linear fractional transformation of the normal coordinates at every point. * NATIONAL, RESEARCH FULLOW IN MATHIMATICS. 1 Cf. 0. Veblen, these PROCEXDINGS, 8, 1922, p. 192. 2 H. Weyl, Gottinger Nachrichten, 1921, p. 99. 3 A type of normal coordinates invariant under the change (1.1) has been given by 0. Veblen and J. M. Thomas in these PROCEEDINGS, 11, 1925, p. 204. 4 0. Veblen, "Remarks...
متن کاملFactorable Congruences and Strict Refinement
We show that universal algebras with factorable congruences such as rings with 1 and semirings with 0 and 1 enjoy some of the properties of universal algebras whose congruence lattices are distributive, such as the strict refinement property and a variant of Jónsson’s lemma. A universal algebra A is said to have factorable congruences if whenever A ∼= B × C and θ is a congruence on A, then θ = ...
متن کاملArc consistency for factorable relations
An optimal arc consistency algorithm AC-4 was given by Mohr and Henderson [8]. AC4 has cost 0(ea), and cost (na) for scene labelling. Although their algorithm is indeed optimal, under certain conditions a constraint satisfaction problem can be transformed into a less complex problem. In this paper, we present conditions and mechanisms for such transformations, and show how to factor relations i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Royal Society of Edinburgh
سال: 1914
ISSN: 0370-1646
DOI: 10.1017/s0370164600013249