nondegenerate

简明释义

英[ˌnɒndɪˈdʒenərət]美[nɑːndɪdʒənəˈreɪt]

非简并

非退化

英英释义

单词用法

同义词

反义词

例句

1.Moreover, when A is a nondegenerate, symmetric and copositive plus matrix, the sequence converges to a solution of the problem.

此外，当矩阵为非退化对称双正加阵时，该序列收敛。

2.The thermal stability, disturbing stability and the differences between degenerate and nondegenerate modes are also discussed.

还进一步讨论了这种谐振腔的热稳定性、微扰稳定性以及简并模与非简并模之间的区别。

3.The thermal stability, disturbing stability and the differences between degenerate and nondegenerate modes are also discussed.

还进一步讨论了这种谐振腔的热稳定性、微扰稳定性以及简并模与非简并模之间的区别。

4.For a triangle to be nondegenerate, the sum of the lengths of any two sides must be greater than the length of the third side.

为了使三角形成为非简并的，任意两边的长度之和必须大于第三边的长度。

5.The nondegenerate conic sections include ellipses, hyperbolas, and parabolas.

非简并的圆锥曲线包括椭圆、双曲线和抛物线。

6.In statistics, a nondegenerate distribution has variance greater than zero.

在统计学中，非简并的分布的方差大于零。

7.A nondegenerate matrix has a non-zero determinant.

一个非简并的矩阵的行列式不为零。

8.In quantum mechanics, a state is considered nondegenerate if it has a unique energy level.

在量子力学中，如果一个状态具有唯一的能量水平，则该状态被认为是非简并的。

作文

In the field of mathematics and physics, the term nondegenerate refers to a situation or condition where certain properties or structures maintain their integrity and do not collapse into a simpler or less complex form. This concept is particularly important in various branches of study, including geometry, linear algebra, and quantum mechanics. Understanding the meaning and implications of nondegenerate can greatly enhance our comprehension of complex systems and their behaviors.To illustrate this concept, let us consider the example of a nondegenerate conic section in geometry. A conic section can be classified as either degenerate or nondegenerate. A degenerate conic might represent a single point or a pair of intersecting lines, while a nondegenerate conic, such as an ellipse, parabola, or hyperbola, retains its distinct shape and properties. The distinction between these two types is crucial for understanding the behavior of curves and their applications in real-world scenarios.In linear algebra, the concept of a nondegenerate matrix is essential when solving systems of equations. A matrix is considered nondegenerate if it has an inverse, which implies that its determinant is non-zero. This property ensures that the system of equations represented by the matrix has a unique solution. Conversely, a degenerate matrix, which has a determinant of zero, indicates that the system may have no solutions or infinitely many solutions. Thus, recognizing whether a matrix is nondegenerate or degenerate is fundamental for anyone working with linear systems.Moving on to quantum mechanics, the concept of nondegenerate energy levels plays a significant role in understanding atomic and molecular structures. In this context, energy levels are said to be nondegenerate if each level corresponds to a unique quantum state. This uniqueness is vital for predicting the behavior of particles and understanding phenomena such as electron transitions and spectral lines. When energy levels are degenerate, multiple quantum states share the same energy, leading to complexities in predictions and interpretations.The importance of nondegenerate structures extends beyond pure mathematics and physics; it also finds applications in engineering, computer science, and even economics. For instance, in optimization problems, ensuring that a function is nondegenerate can lead to more reliable solutions and better performance in algorithms. In economics, nondegenerate equilibria can signify stable market conditions, whereas degenerate cases may indicate market failures or inefficiencies.In conclusion, the term nondegenerate encapsulates a critical aspect of various scientific and mathematical disciplines. Its significance lies in maintaining the integrity and complexity of structures, whether they be geometric figures, matrices, energy levels, or economic models. By grasping the meaning of nondegenerate, we can deepen our understanding of the underlying principles that govern complex systems and enhance our ability to analyze and solve problems across diverse fields. As we continue to explore the intricacies of the universe, the concept of nondegenerate will remain a cornerstone in our quest for knowledge and understanding.

在数学和物理学领域，术语nondegenerate指的是某些属性或结构保持其完整性并且不会崩溃为更简单或不那么复杂的形式的情况或条件。这个概念在多个研究领域中尤为重要，包括几何、线性代数和量子力学。理解nondegenerate的含义及其影响可以大大增强我们对复杂系统及其行为的理解。为了说明这一概念，让我们考虑几何中非退化圆锥曲线的例子。圆锥曲线可以被分类为退化或nondegenerate。退化圆锥可能代表一个单点或一对相交的直线，而nondegenerate圆锥，如椭圆、抛物线或双曲线，则保持其独特的形状和属性。这两种类型之间的区别对于理解曲线的行为及其在现实场景中的应用至关重要。在线性代数中，nondegenerate矩阵的概念在解决方程组时至关重要。如果一个矩阵具有逆矩阵，则被认为是nondegenerate，这意味着它的行列式非零。这个属性确保了由矩阵表示的方程组有唯一解。相反，行列式为零的退化矩阵表明该系统可能没有解或有无穷多解。因此，识别一个矩阵是nondegenerate还是退化对任何处理线性系统的人来说都是基础。转向量子力学，nondegenerate能级的概念在理解原子和分子结构中起着重要作用。在这种情况下，如果每个能级对应于唯一的量子态，则称能级为nondegenerate。这种唯一性对于预测粒子的行为和理解电子跃迁及光谱线等现象至关重要。当能级是退化的时，多重量子态共享相同的能量，导致预测和解释的复杂性。nondegenerate结构的重要性不仅限于纯数学和物理学；它在工程、计算机科学甚至经济学中也有应用。例如，在优化问题中，确保一个函数是nondegenerate可以导致更可靠的解决方案和更好的算法性能。在经济学中，nondegenerate均衡可以表示稳定的市场条件，而退化案例可能表明市场失灵或低效。总之，术语nondegenerate概括了各种科学和数学学科的一个关键方面。它的重要性在于保持结构的完整性和复杂性，无论它们是几何图形、矩阵、能级还是经济模型。通过掌握nondegenerate的含义，我们可以加深对支配复杂系统的基本原则的理解，并增强我们在各个领域分析和解决问题的能力。随着我们继续探索宇宙的复杂性，nondegenerate的概念将始终是我们追求知识和理解的基石。