indecomposable

简明释义

英[ˌɪndiːkəmˈpəʊzəb(ə)l]美[ˌɪndiːkəmˈpoʊzəbl]

adj. 不能分解的；[数] 不可分的

英英释义

单词用法

同义词

反义词

例句

1.This is an indecomposable substance.

这是不能分解的物质。

2.Secondly, we discuss the problem of decomposing a nonnegative matrix into a product of fully indecomposable nonnegative matrices in chapter 2.

其次，在第二章中，我们讨论了将一个非负矩阵分解成有限多个完全不可分非负阵的乘积的问题。

3.Secondly, we discuss the problem of decomposing a nonnegative matrix into a product of fully indecomposable nonnegative matrices in chapter 2.

其次，在第二章中，我们讨论了将一个非负矩阵分解成有限多个完全不可分非负阵的乘积的问题。

4.The artist's work was seen as indecomposable, with each element contributing to a unified whole.

这位艺术家的作品被视为不可分解的，每个元素都为统一的整体做出了贡献。

5.A prime number is an example of an indecomposable number in arithmetic.

质数是算术中不可分解的数字的一个例子。

6.In mathematics, an indecomposable structure is one that cannot be broken down into simpler components.

在数学中，不可分解的结构是指无法拆分成更简单的组成部分。

7.In chemistry, some compounds are indecomposable under normal conditions.

在化学中，有些化合物在正常条件下是不可分解的。

8.The indecomposable nature of the material makes it ideal for construction.

这种材料的不可分解性使其非常适合用于建筑。

作文

In the realm of mathematics and abstract algebra, the term indecomposable refers to a structure that cannot be broken down into simpler components. This concept is particularly significant when discussing modules or representations. A module is considered indecomposable if it cannot be expressed as a direct sum of two non-trivial submodules. Understanding indecomposable structures is crucial for mathematicians as it helps to classify objects and understand their properties in a more profound way.For instance, in linear algebra, an indecomposable representation of a group is one that does not decompose into smaller representations. This means that the representation is 'atomic' in nature, serving as a building block for further studies in the field. The significance of indecomposable modules extends beyond theoretical mathematics; they have practical applications in areas such as physics and computer science, where systems can often be modeled using mathematical structures.Consider the analogy of a complex machine. If we think of a machine as a whole, it may seem simple at first glance. However, upon closer inspection, we realize it consists of numerous parts working together. Some machines are designed in such a way that they are indecomposable; that is, their functionality cannot be split into smaller, independent units without losing their overall purpose. For example, a smartphone is an indecomposable device because its various functions—communication, computation, and entertainment—are all integrated into one unit. If we were to separate these functions, we would lose the essence of what makes a smartphone valuable.In contrast, consider a set of building blocks. Each block can be seen as a decomposable unit, where you can take apart combinations to create new structures. This illustrates the difference between indecomposable and decomposable systems. In many cases, being indecomposable is a strength, as it implies robustness and resilience. For example, in biology, certain organisms exhibit indecomposable traits that allow them to survive in harsh environments. Their ability to maintain integrity despite external pressures showcases the advantages of being indecomposable.Moreover, the notion of indecomposable can also be applied metaphorically in life. Individuals who possess indecomposable character traits—such as resilience, determination, and integrity—tend to withstand challenges and adversities. They do not break down under pressure but instead emerge stronger and more unified. Such individuals serve as role models, demonstrating that being indecomposable is not just a mathematical concept but a valuable life lesson.In conclusion, the term indecomposable carries significant weight across various disciplines. Whether in mathematics, engineering, biology, or personal development, understanding the implications of being indecomposable allows us to appreciate complexity and robustness in both theoretical constructs and real-world applications. As we delve deeper into the intricacies of systems, recognizing the role of indecomposable elements will enhance our comprehension and foster innovation in our approaches to problem-solving.

在数学和抽象代数的领域中，术语indecomposable指的是一种结构，无法被分解为更简单的组成部分。这个概念在讨论模或表示时特别重要。如果一个模被认为是indecomposable，那么它不能被表示为两个非平凡子模的直接和。理解indecomposable结构对数学家来说至关重要，因为它有助于对对象进行分类，并更深入地理解其属性。例如，在线性代数中，一个群的indecomposable表示是一个无法分解为更小表示的表示。这意味着该表示在本质上是“原子”的，作为进一步研究该领域的构建块。indecomposable模的意义超越了理论数学；它们在物理学和计算机科学等领域具有实际应用，在这些领域中，系统通常可以使用数学结构建模。考虑复杂机器的类比。如果我们把一台机器看作一个整体，乍一看它可能显得简单。然而，仔细观察，我们意识到它由许多部分共同工作。有些机器设计成indecomposable，也就是说，它们的功能无法分拆为更小的独立单元而不失去整体目的。例如，智能手机就是一个indecomposable设备，因为它的各种功能——通信、计算和娱乐——都集成在一个单元中。如果我们将这些功能分离，我们就会失去智能手机的价值本质。相反，考虑一组积木。每个积木可以视为可分解单元，您可以拆分组合以创建新结构。这说明了indecomposable与可分解系统之间的区别。在许多情况下，成为indecomposable是一种优势，因为它暗示着稳健性和韧性。例如，在生物学中，某些生物表现出indecomposable特征，使它们能够在恶劣环境中生存。它们在外部压力下保持完整的能力展示了成为indecomposable的优势。此外，indecomposable的概念也可以隐喻性地应用于生活。具备indecomposable性格特征的个体——如韧性、决心和正直——往往能够承受挑战和逆境。他们在压力下不会崩溃，而是变得更强大、更团结。这些个体作为榜样，展示了成为indecomposable不仅仅是一个数学概念，而是一个宝贵的人生课程。总之，术语indecomposable在各个学科中都具有重要意义。无论是在数学、工程、生物学还是个人发展中，理解成为indecomposable的含义使我们能够欣赏理论构造和现实应用中的复杂性和稳健性。当我们深入研究系统的复杂性时，认识到indecomposable元素的作用将增强我们的理解，并促进我们在解决问题方法上的创新。