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A vector space over a field F is a set V together with two binary operations.
域 F 上的向量空间是集合 V 再加上两个二元运算 。
A construction of authentication codes with arbitration from subspace of vector space over finite fields is presented, the parameters of the code are computed.
摘要利用有限域上向量空间的子空间构作了一个具有仲裁的认证码,计算了这个码的参数。
More generally, the term may refer to a seven-dimensional vector space over any field, such as a seven-dimensional complex vector space, which has 14 real dimensions.
These operations turn the quotient space V/N into a vector space over K with N being the zero class,.
这些运算将商空间V/N转化为K上一个向量空间,N成为零类。
If V is a vector space over the field F, the general linear group of V, written GL(V) or Aut(V), is the group of all automorphisms of V, i.e. the set of all bijective linear transformations V -> V, together with functional composition as group operation.
如果 V 是在域 F 上的向量空間,V 的一般線性群,寫為GL(V)或Aut(V),是 V 的所有自同構的群,就是說所有雙射線性變換 V -> V 的集合,和與之一起的函數復合作為群運算。
He is perhaps best known for the Hamel basis, published in 1905, when he made an early and explicit use of the Axiom of Choice to construct a basis for the real numbers as a vector space over the rational numbers.
Topics in this area include: Configurations Line arrangements Hyperplane arrangements Buildings An oriented matroid is a mathematical structure that abstracts the properties of directed graphs and of arrangements of vectors in a vector space over an ordered field (particularly for partially ordered vector spaces).
For example she published On Witt's theorem for nonalternating symmetric bilinear forms over a field of characteristic 2 in 1964 and On the invariants of a vector subspace of a vector space over a field of characteristic two in the following year, both publications being in the Proceedings of the American Mathematical Society.
Mathematically they can be specified by 8-tuplets of real numbers, so form an 8-dimensional vector space over the reals, with addition of vectors being the addition in the algebra.
As a quaternion consists of two independent complex numbers, they form a 4-dimensional vector space over the real numbers.
由于四元数由独立的两个复数组成,它们构成实数域上的4维线性空间。
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