characteristic number

简明释义

特性数

英英释义

例句

1.In statistics, the mean can be viewed as a characteristic number 特征数 that summarizes a data set.

在统计学中，均值可以看作是一个特征数 characteristic number，用于总结数据集。

2.In physics, the characteristic number 特征数 can represent various physical constants.

在物理学中，特征数 characteristic number 可以表示各种物理常数。

3.Each element in the periodic table has a unique characteristic number 特征数 that defines its atomic structure.

周期表中的每个元素都有一个独特的特征数 characteristic number，定义了其原子结构。

4.In mathematics, a prime number is often considered a characteristic number 特征数 for its unique properties.

在数学中，质数常被认为是一个特征数 characteristic number，因为它具有独特的性质。

5.The characteristic number 特征数 of a polynomial can help determine its roots.

多项式的特征数 characteristic number 可以帮助确定其根。

作文

In mathematics, particularly in the field of number theory, the term characteristic number refers to a specific value that defines certain properties of a mathematical structure. It plays a crucial role in various areas such as algebra, geometry, and even in applied sciences. Understanding characteristic number is essential for students who wish to delve deeper into advanced mathematics and its applications.To illustrate the concept, let us consider a simple example from linear algebra. The characteristic number, often called the eigenvalue, is derived from a matrix. When we calculate the determinant of a matrix subtracted by a scalar multiple of the identity matrix, we obtain a polynomial equation. The roots of this equation are the characteristic numbers or eigenvalues of the matrix. These values provide insight into the behavior of linear transformations represented by the matrix.Moreover, characteristic numbers can also be found in the context of differential equations. For instance, when solving a second-order differential equation, one might encounter a characteristic equation. The solutions to this equation yield characteristic numbers that help determine the general solution of the differential equation. This application highlights the importance of characteristic numbers in understanding dynamic systems and their behaviors over time.In physics, the concept of characteristic number extends beyond pure mathematics. For example, in thermodynamics, the characteristic number can refer to dimensionless quantities that characterize the flow of fluids, such as the Reynolds number. This number helps predict flow patterns in different fluid dynamics scenarios and is critical for engineers and scientists working in this field.Furthermore, in statistics, characteristic numbers are used to summarize data sets. Measures such as the mean, median, and mode serve as characteristic numbers that provide insights into the distribution and central tendency of data. By analyzing these numbers, researchers can draw conclusions about the overall trends within a dataset, making them invaluable in fields ranging from social sciences to market research.In conclusion, the term characteristic number encompasses various meanings across different mathematical and scientific disciplines. Whether it is through eigenvalues in linear algebra, solutions in differential equations, dimensionless quantities in fluid dynamics, or summary statistics in data analysis, characteristic numbers serve as vital tools for understanding complex systems. For students and professionals alike, mastering the concept of characteristic number opens doors to deeper insights and innovative solutions in their respective fields. As we continue to explore the intricacies of mathematics and its applications, the significance of characteristic numbers will undoubtedly remain a cornerstone of our understanding.

在数学中，尤其是在数论领域，术语特征数指的是定义某些数学结构特性的特定值。它在代数、几何甚至应用科学等多个领域中发挥着至关重要的作用。理解特征数对希望深入研究高级数学及其应用的学生至关重要。为了说明这一概念，让我们考虑线性代数中的一个简单例子。特征数，通常称为特征值，是从矩阵中导出的。当我们计算一个矩阵减去一个标量倍数的单位矩阵的行列式时，我们得到一个多项式方程。这个方程的根就是矩阵的特征数或特征值。这些值提供了关于由矩阵表示的线性变换行为的洞察。此外，特征数也可以在微分方程的上下文中找到。例如，在求解二阶微分方程时，可能会遇到一个特征方程。这个方程的解产生的特征数有助于确定微分方程的一般解。这一应用突显了特征数在理解动态系统及其随时间变化的行为中的重要性。在物理学中，特征数的概念超越了纯数学。例如，在热力学中，特征数可以指特征流体流动的无量纲量，如雷诺数。这个数值有助于预测不同流体动力学场景中的流动模式，对于在该领域工作的工程师和科学家至关重要。此外，在统计学中，特征数用于总结数据集。诸如均值、中位数和众数等度量作为特征数提供了对数据分布和集中趋势的洞察。通过分析这些数字，研究人员可以得出关于数据集中整体趋势的结论，使其在社会科学到市场研究等多个领域中不可或缺。总之，术语特征数在不同的数学和科学学科中包含了多种含义。无论是通过线性代数中的特征值、微分方程中的解、流体动力学中的无量纲量，还是在数据分析中的汇总统计，特征数都作为理解复杂系统的重要工具。对于学生和专业人士而言，掌握特征数的概念为他们在各自领域的深入洞察和创新解决方案打开了大门。随着我们继续探索数学及其应用的复杂性，特征数的重要性无疑将始终是我们理解的基石。