共查询到20条相似文献,搜索用时 93 毫秒
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João Gouveia Roland Grappe Volker Kaibel Kanstantsin Pashkovich Richard Z. Robinson Rekha R. Thomas 《Linear algebra and its applications》2013
In this paper we characterize the slack matrices of cones and polytopes among all nonnegative matrices. This leads to an algorithm for deciding whether a given matrix is a slack matrix. The underlying decision problem is equivalent to the polyhedral verification problem whose complexity is unknown. 相似文献
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A matrix A ∈ Mn(C) is called generalized normal provided that there is a positive definite Hermite matrix H such that HAH is normal. In this paper, these matrices are investigated and their canonical form, invariants and relative properties in the sense of congruence are obtained. 相似文献
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The inertia-preservers of several sets of matrices are identified. The sets include: all real matrices, all complex matrices, triangular matrices, real symmetric matrices and Hermitian matrices. 相似文献
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Ring geometry and the geometry of matrices naturally meet at the ring R := K n×n of (n×n)-matrices with entries in a field K (not necessarily commutative). Our aim is to strengthen the interaction between these disciplines. Below we sketch some results from either side, even though not in their most general form, but in a way that is tailored to our needs. 相似文献
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Hock Ong 《Linear algebra and its applications》1976,15(2):119-151
Let F be a field, F1 be its multiplicative group, and = {H:H is a subgroup of F1 and there do not exist a, b?F1 such that Ha+b?H}. Let Dn be the dihedral group of degree n, H be a nontrivial group in , and τn(H) = {α = (α1, α2,…, αn):αi?H}. For σ?Dn and α?τn(H), let P(σ, α) be the matrix whose (i,j) entry is αiδiσ(j) (i.e., a generalized permutation matrix), and . Let Mn(F) be the vector space of all n×n matrices over F and P(Dn, H) = {T:T is a linear transformation on Mn (F) to itself and T(P(Dn, H)) = P(Dn, H)}. In this paper we classify all T in P(Dn, H) and determine the structure of the group P(Dn, H) (Theorems 1 to 4). An expository version of the main results is given in Sec. 1, and an example is given at the end of the paper. 相似文献
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Masha Vlasenko 《Indagationes Mathematicae》2018,29(5):1411-1424
We prove a number of -adic congruences for the coefficients of powers of a multivariate polynomial with coefficients in a ring of characteristic zero. If the Hasse–Witt operation is invertible, our congruences yield -adic limit formulae which conjecturally describe the Gauss–Manin connection and the Frobenius operator on the unit-root crystal attached to . As a second application, we associate with formal group laws over . Under certain assumptions these formal group laws are coordinalizations of the Artin–Mazur functors. 相似文献
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M. H. Hosseini 《Journal of Mathematical Sciences》2007,140(2):333-339
It is proved that a (C 1, C 2)-Hölder valuation is (2, α)-equivalent to classical valuation on the set of matrices over a skew field and on the set of cubic matrices over a field. These results provide an extension of the Garcia theorem. 相似文献
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Henry Minc 《Linear and Multilinear Algebra》2013,61(1):85-90
Let A be an irreducible matrix with index of imprimitivity h is shown that there exists a permutation matrix P such that PAPt is in a superdiagonal block form with k nonzero blocks if and only if k divides h It is also shown that a matrix in a superdiagonal block form without zero rows or columns is irreducible if and only if the product of the superdiagonal nonzero blocks is irreducible. 相似文献
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In this note, two classes of quasi-difference matrices, -QDM and -QDM, are constructed. Combining the known results of quasi-difference matrices and difference matrices, a new short disproof of Euler’s conjecture on mutually orthogonal Latin squares is given. 相似文献
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LetD be a division ring which possesses an involution a → α . Assume that
is a proper subfield ofD and is contained in the center ofD. It is pointed out that ifD is of characteristic not two, D is either a separable quadratic extension of F or a division ring of generalized quaternions
over F and that if D is of characteristic two,D is a separable quadratic extension ofF. Thus the trace map Tr:D → F, a → a + a is always surjective, which is formerly posed as an assumption in the fundamental theorem of n×n hermitian
matrices overD when n ≥ 3 and now can be deleted. WhenD is a field, the fundamental theorem of 2 × 2 hermitian matrices overD has already been proved. This paper proves the fundamental theorem of 2×2 hermitian matrices over any division ring of generalized
quaternions of characteristic not two
This research was completed during a visit to the Academy of Mathematics and System Sciences, Chinese Academy of Sciences. 相似文献
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Abhijit S. Ranjekar 《Proceedings Mathematical Sciences》1999,109(4):385-388
In this note we discuss the inverse spectral theory for Schrödinger matrices, in particular a conjecture of Gesztesy-Simon [1] on the number of distinct iso-spectral Schrödinger matrices. We consider 3 × 3 matrices and obtain counter examples to their conjecture. 相似文献
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《Indagationes Mathematicae (Proceedings)》1989,92(4):465-470
For all positive a the point spectrum of the (C, α) matrix is determined, where the matrix is regarded as an operator on certain Banach sequence spaces. In particular the point spectrum is obtained in the spaces Ip(X), with 1<p≤∞, where X is a Banach space. 相似文献