generating set

简明释义

1. 发电设备; 2. 发电机;

英英释义

例句

1.Our company invested in a solar-powered generating set to reduce carbon emissions.

我们公司投资了一个太阳能发电机组以减少碳排放。

2.The generating set was installed to ensure continuous power supply during peak hours.

安装了发电机组以确保高峰时段的持续供电。

3.The construction site required a robust generating set to power heavy machinery.

施工现场需要一个强大的发电机组来为重型机械供电。

4.The engineer designed a new generating set to improve energy efficiency.

工程师设计了一个新的发电机组以提高能源效率。

5.During the power outage, we relied on our portable generating set for electricity.

在停电期间，我们依靠便携式发电机组提供电力。

作文

In the world of mathematics, particularly in the field of linear algebra, the concept of a generating set plays a crucial role in understanding vector spaces. A generating set is essentially a collection of vectors in a vector space such that any vector in that space can be expressed as a linear combination of the vectors in the generating set. This means that by scaling and adding these vectors together, we can create every possible vector within that space. To illustrate this concept, let’s consider a simple example. Imagine we have a two-dimensional space, which can be represented on a plane. If we take two non-parallel vectors, say vector A and vector B, these vectors can serve as a generating set for the entire two-dimensional space. Any point on this plane can be reached by appropriately scaling and combining these two vectors. Therefore, the pair {A, B} forms a generating set for the vector space R².The importance of identifying a generating set cannot be understated. In practical applications, such as computer graphics, physics, and engineering, understanding how to generate all possible states or configurations of a system from a finite set of basis vectors is essential. For instance, in computer graphics, the ability to manipulate shapes and images often relies on a generating set of transformations, such as rotations and translations, to achieve complex visual effects.Moreover, the concept extends beyond just two dimensions. In higher-dimensional spaces, a generating set can consist of more than two vectors. For example, in three-dimensional space, a set of three vectors that are not coplanar can serve as a generating set for R³. This versatility allows mathematicians and scientists to explore multidimensional phenomena, making it an invaluable tool in various fields.In addition to its mathematical significance, the idea of a generating set can also be applied metaphorically in other domains. For instance, in the realm of social sciences, one might consider a generating set of ideas or beliefs that shape a community's culture. Just as in mathematics, where a few vectors can generate an entire space, a small number of influential ideas can shape the values and behaviors of a society. This analogy highlights the interconnectedness of concepts across different fields, illustrating how foundational principles can manifest in diverse contexts.In conclusion, the concept of a generating set is fundamental in both mathematics and its applications. It provides a framework for understanding how complex systems can be derived from simpler components. Whether in the realm of linear algebra or in broader philosophical discussions, the idea of a generating set encourages us to think about the underlying structures that form the basis of our understanding. As we continue to explore and apply this concept, we gain deeper insights into the nature of spaces, whether they be mathematical, physical, or social. Thus, the generating set remains a powerful tool in our quest for knowledge and comprehension.

在数学的世界中，特别是在线性代数领域，生成集的概念在理解向量空间时起着至关重要的作用。生成集本质上是一个向量集合，在该向量空间中，任何向量都可以表示为生成集中向量的线性组合。这意味着通过缩放和相加这些向量，我们可以创建该空间内的每一个可能向量。为了说明这个概念，让我们考虑一个简单的例子。想象一下我们有一个二维空间，可以在平面上表示。如果我们取两个不平行的向量，比如向量A和向量B，这些向量可以作为整个二维空间的生成集。在这个平面上的任何点都可以通过适当缩放和组合这两个向量来达到。因此，{A，B}这一对形成了向量空间R²的生成集。识别生成集的重要性不容小觑。在计算机图形学、物理学和工程等实际应用中，理解如何从有限的基向量集合生成系统的所有可能状态或配置至关重要。例如，在计算机图形学中，操纵形状和图像的能力通常依赖于一组变换的生成集，如旋转和平移，以实现复杂的视觉效果。此外，这个概念不仅限于二维。 在更高维度的空间中，一个生成集可以由多个向量组成。例如，在三维空间中，一组不共面的三个向量可以作为R³的生成集。这种多样性使得数学家和科学家能够探索多维现象，使其成为各个领域中不可或缺的工具。除了其数学意义外，生成集的思想也可以在其他领域中隐喻性地应用。例如，在社会科学领域，人们可能会考虑一组塑造社区文化的思想或信念的生成集。正如在数学中，少数向量可以生成整个空间一样，少数影响力大的思想可以塑造一个社会的价值观和行为。这种类比突显了不同领域之间概念的相互联系，说明基础原则如何在多样的背景中表现出来。总之，生成集的概念在数学及其应用中是基础性的。它提供了一个框架，用于理解复杂系统如何从更简单的组成部分中派生而来。无论是在线性代数的领域还是在更广泛的哲学讨论中，生成集的思想鼓励我们思考形成我们理解基础的潜在结构。随着我们继续探索和应用这一概念，我们将深入洞察空间的本质，无论是数学、物理还是社会。因此，生成集在我们追求知识和理解的过程中仍然是一个强大的工具。