antisymmetric

简明释义

英[/ˌæntiˈsɪmɛtrɪk/]美[/ˌæntiˈsɪmɛtrɪk/]

adj. 反对称的

英英释义

单词用法

同义词

反义词

例句

1.The definition of relation, relations properties about to reflexive and irreflexive, symmetric and antisymmetric and transitive, and its application in computer science has been recited.

介绍了关系的定义、关系的自反性和反自反性、对称性和反对称性、传递性五条性质，及其在计算机领域中的应用。

2.The symmetric perturbation is of real mode and the antisymmetric is of complex mode.

对称部分是实模态摄动，反对称部分是复模态摄动。

3.According to the planar constraints, we proved that the product of the fundamental matrix and the homography matrix of an image pair is an antisymmetric matrix.

根据两幅图像中的平面约束，证明了图像对的基础矩阵和同形矩阵的乘积具有反对称的性质。

4.Particles, such as electrons, requiring antisymmetric wave functions are called fermions.

要求反对称波函数的粒子，如电子，叫做费米子。

5.The various anisotropic spin interactions which can be represented by the rank two tensors are decomposed into isotropic, symmetric, and antisymmetric constituents.

核自旋之间的各种各向异性相互作用都能用二阶张量表示，这些张量可分解成各向同性、对称以及反对称分量。

6.The definition of relation, relations properties about to reflexive and irreflexive, symmetric and antisymmetric and transitive, and its application in computer science has been recited.

介绍了关系的定义、关系的自反性和反自反性、对称性和反对称性、传递性五条性质，及其在计算机领域中的应用。

7.This paper demonstrates some methods of the building of the real antisymmetric matrix and some detailed demonstrate.

给出了实反对称矩阵的若干构建方法及部分方法的证明。

8.The concept of antisymmetric relations is important in order theory.

在序理论中，反对称关系的概念是非常重要的。

9.An antisymmetric function has the property that f(x, y) = -f(y, x).

一个反对称函数具有这样的性质：f(x, y) = -f(y, x)。

10.In mathematics, a relation R is called antisymmetric when for all a and b, if aRb and bRa, then a must be equal to b.

在数学中，当对于所有的a和b，如果aRb且bRa，则a必须等于b时，关系R被称为反对称。

11.In physics, certain forces are modeled using antisymmetric tensors to describe their properties.

在物理学中，某些力使用反对称张量来建模，以描述其特性。

12.The matrix is antisymmetric if its transpose is equal to its negative.

如果一个矩阵的转置等于其负值，则该矩阵是反对称的。

作文

In mathematics, particularly in the field of algebra and geometry, the concept of antisymmetric plays a crucial role in understanding various structures and relationships. An operation or relation is termed antisymmetric if it satisfies a specific property: for any two elements a and b, if both a is related to b and b is related to a, then a must be equal to b. This definition might seem abstract at first, but it has profound implications in different mathematical contexts.To illustrate the idea of antisymmetric, consider the example of a simple ordering of numbers. In the case of the less-than-or-equal-to relation (≤), we can see that if a ≤ b and b ≤ a, it follows that a must equal b. Therefore, this relation is antisymmetric. On the other hand, if we take the less-than relation (<), it is not antisymmetric because it does not allow for equality; if a < b and b < a cannot hold simultaneously unless a and b are distinct.The significance of antisymmetric relations extends beyond mere number comparisons. For instance, in linear algebra, when dealing with matrices, a matrix is described as antisymmetric if its transpose is equal to its negative. This means that for every element in the matrix, the entry at position (i,j) is the negative of the entry at position (j,i). Such matrices have unique properties, such as having eigenvalues that are either zero or purely imaginary, which is essential in physics and engineering applications.Furthermore, the concept of antisymmetric can also be observed in graph theory. In directed graphs, an edge from vertex A to vertex B indicates a relationship, and if there is also an edge from B to A, the relationship can be considered antisymmetric if A and B are the same vertex. This property helps in defining certain types of relations and functions in discrete mathematics.In the realm of computer science, antisymmetric relations are used in algorithms and data structures. For instance, when designing a database schema, understanding whether a relationship between entities is antisymmetric can help in optimizing queries and ensuring data integrity. Additionally, in programming languages, the concept of antisymmetric can be applied in defining function behaviors, particularly in sorting algorithms where maintaining a consistent order is critical.In conclusion, the term antisymmetric serves as a foundational concept across various branches of mathematics and its applications. Whether it is in the study of relations, matrices, graphs, or algorithms, recognizing and applying the property of antisymmetric enables mathematicians and scientists to build more complex theories and solve intricate problems. By grasping the essence of this term, one can appreciate the elegance and interconnectedness of mathematical principles that govern our understanding of the world around us.

在数学中，特别是在代数和几何领域，antisymmetric（反对称）这一概念在理解各种结构和关系时起着至关重要的作用。当一个操作或关系被称为antisymmetric时，它满足一个特定的性质：对于任何两个元素a和b，如果a与b相关且b与a相关，则a必须等于b。这个定义乍一看可能显得抽象，但它在不同的数学背景下具有深远的意义。为了说明antisymmetric的概念，考虑一个简单的数字排序的例子。在小于或等于的关系（≤）中，我们可以看到，如果a ≤ b且b ≤ a，那么a必然等于b。因此，这个关系是antisymmetric的。另一方面，如果我们取小于关系（<），它就不是antisymmetric的，因为它不允许相等；如果a < b且b < a不能同时成立，除非a和b是不同的。Antisymmetric关系的重要性超越了简单的数字比较。例如，在线性代数中，当处理矩阵时，如果一个矩阵的转置等于其负值，则该矩阵被描述为antisymmetric。这意味着对于矩阵中的每个元素，位置(i,j)的条目是位置(j,i)的条目的负值。这类矩阵具有独特的性质，例如其特征值要么为零，要么为纯虚数，这在物理学和工程应用中至关重要。此外，antisymmetric的概念也可以在图论中观察到。在有向图中，从顶点A到顶点B的边表示一种关系，如果也存在从B到A的边，则如果A和B是同一个顶点，则该关系可以被视为antisymmetric。这一属性有助于在离散数学中定义某些类型的关系和函数。在计算机科学领域，antisymmetric关系被用于算法和数据结构。例如，在设计数据库模式时，理解实体之间的关系是否为antisymmetric可以帮助优化查询并确保数据完整性。此外，在编程语言中，antisymmetric的概念可以应用于定义函数行为，特别是在排序算法中，保持一致的顺序至关重要。总之，术语antisymmetric作为一个基础概念，在数学及其应用的各个分支中发挥着作用。无论是在研究关系、矩阵、图形还是算法时，识别和应用antisymmetric的属性使数学家和科学家能够构建更复杂的理论并解决复杂的问题。通过掌握这一术语的本质，人们可以欣赏到支配我们对周围世界理解的数学原理的优雅与相互联系。