منابع مشابه
Essentially Hermitian matrices revisited
The following case of the Determinantal Conjecture of Marcus and de Oliveira is established. Let A and C be hermitian n × n matrices with prescribed eigenvalues a1, . . . , an and c1, . . . , cn, respectively. Let κ be a non-real unimodular complex number, B = κC, bj = κcj for j = 1, . . . , n. Then det(A− B) ∈ co 8< : n Y j=1 (aj − bσ(j)); σ ∈ Sn 9= ; , where Sn denotes the group of all permut...
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Signatures of quadratic forms over formally real fields have been generalized in [BP2] to hermitian forms over central simple algebras with involution over such fields. This was achieved by means of an application of Morita theory and a reduction to the quadratic form case. A priori, signatures of hermitian forms can only be defined up to sign, i.e., a canonical definition of signature is not p...
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We will determine (up to equivalence) all of the integral positive definite Hermitian lattices in imaginary quadratic fields of class number 1 that represent all positive integers.
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We investigate the following two problems on a hermitian form Φ over an algebraic number field: (1) classification of Φ over the ring of algebraic integers; (2) hermitian Diophantine equations. The same types of problems for quadratic forms were treated in the author’s previous articles. Here we discuss the hermitian case. Problem (2) concerns an equation ξΦ · ξ = Ψ , where Φ and Ψ represent he...
متن کاملε-Nets for Halfspaces Revisited∗
Given a set P of n points in R3, we show that, for any ε > 0, there exists an ε-net of P for halfspace ranges, of size O(1/ε). We give five proofs of this result, which are arguably simpler than previous proofs [?, ?, ?]. We also consider several related variants of this result, including the case of points and pseudo-disks in the plane.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1983
ISSN: 0021-8693
DOI: 10.1016/0021-8693(83)90126-6