is called a polynomial of degree if and only if, for any , where belong to and . The elements are called coefficients of the polynomial. In the above definition is assumed to be a non-negative integer. If (i.e., the coefficients are all equal to zero), then the degree of is conven...
Let A be a (not necessarily associative) algebra finite dimensional over an infinite field k, and A{x} its algebra of polynomial functions in the indeterminate x. Separable polynomial functions in A{x} are defined as polynomial functions which have the maximum possible finite number of distinct...
Commutative algebra is one of the branches of algebra that studies the commutative rings and their ideals. The algebraic number theory, as well as the algebraic geometry, depends on commutative algebra. It includes rings of algebraic integers, polynomial rings, and so on. Many other mathematics ar...
Mathematicsany of several algebraic systems, esp. a ring in which elements can be multiplied by real or complex numbers (linear algebra)as well as by other elements of the ring. Mathematicsany special system of notation adapted to the study of a special system of relationship:algebra of classes...
Definition Equivalence Relation An equivalence relation on a set S is a set R of ordered pairs of elements of S such that 1. (a, a) ∈R for all a∈S (reflexive property). 2. (a, b) ∈R implies (b, a) ∈R (symmetric property). ...
Definition. The distinct lines where each is a unit vector, are said to beequiangularif for some and all Question. What is the maximum size of a set of equiangular lines in? That is not easy to answer in general, but there is a decent upper bound on the size of such sets that we ...
Definition: 向量空间 V 中,任何一组满足线性无关的向量 v_1,…,v_m ,且 span(v_1,…,v_m)=V 都是V 的基Theorem: 基底判定: v_1,…,v_m 是V 的一组基 \Leftrightarrow \forall v\in V,\exists !a_1,…,a_m\in F,not\ all\ a_i\ =0,v=\sum_{i=1}^ma_iv_i ...
The symmetric group\mathfrak{S}_{n}acts on the polynomial ring\mathbb{F}[X]:=\mathbb{F}[x_{1},\ldots,x_{n}]by permuting the variables, and the 0-Hecke algebraHn(0) acts on\mathbb{F}[X]via theDemazure operatorsπ1,…,πn−1, where ...
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Factor of a Polynomial 多项式因子 Factor Theorem 因子定理 Factorial 阶乘 Factoring Rules 阶乘规则 Focal Radius 焦距 Foci of an Ellipse 椭圆焦点 Foci of a Hyperbola 双曲线焦点 Focus 焦点 Focus of a Parabola 抛物线焦点 Formula 公式 Fractional Equation 分数方程 Fractional Exponents 分数指数 Fractional ...