diagonalization

简明释义

英[daɪˌæɡənəlaɪˈzeɪʃən]美[daɪˌæɡənəlɪˈzeʃən]

n. [数] 对角化；对角线化

英英释义

单词用法

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例句

1.The squeezed state of single module is discussed frome aspects of squeezed operator, squeezed coherent state, squeezed transformation, the diagonalization of Hamiltionian, and so on.

从压缩算符、压缩相干态、压缩变换与哈密顿量的对角化等几个方面对单模压缩态进行了讨论。

2.Successive diagonalization and truncation technique was used to reduce the size of the final Hamiltonian matrix to be diagonalized.

为了降低需要对角化的最终哈密顿矩阵的维数，采用连续对角化截断方法。

3.The parameters are introduced based on the natural stress modes of the displacement element, and the method of matrix H diagonalization was introduced to improve the calculation of the natural.

本文在位移元本征应力模式基础上引进调节参数，同时，利用矩阵H对角化方法计算杂交元应力子空间的本征应力模式，然后由此方便有效地计算特征值，从而大大提高了计算效率。

4.The energy eigenvalues and the squeezed state solutions are obtained by making use of algebraic diagonalization.

利用代数对角化方法，可得到压缩态形式的能量本征态和相应的能量本征值。

5.In the two-sublattice model, the Heisenberg exchange interaction Hamiltonian of the simple ferrimagnetic crystal can be made diagonalization by the use of HP, Fourier and Bogoliubov transformation.

在双子格模型中，运用HP变换、付里叶变换和玻戈留波夫变换，将简单亚铁磁体的海森伯交换作用哈密顿量对角化。

6.The conditions of simultaneous diagonalization of two matrices are given.

给出两个矩阵同时合同对角化与同时相似对角化的一些条件。

7.In this paper we give a necessary and sufficient condition on diagonalization matrix.

本文给出矩阵可对角化的一个充要条件。

8.The paper presents a method for constructing partial hybrid finite element by diagonalization of matrix h.

给出了利用H阵对角化建立部分杂交元的方法。

9.We used diagonalization to solve the differential equations more efficiently.

我们使用对角化来更高效地解决微分方程。

10.The process of diagonalization allows us to simplify complex linear transformations.

通过对角化的过程，我们可以简化复杂的线性变换。

11.The matrix can be simplified through diagonalization, making calculations easier.

通过对角化，矩阵可以被简化，从而使计算变得更容易。

12.In quantum mechanics, diagonalization helps in finding the eigenstates of a system.

在量子力学中，对角化有助于找到系统的本征态。

13.Understanding diagonalization is crucial for advanced studies in linear algebra.

理解对角化对于线性代数的高级研究至关重要。

作文

In the realm of linear algebra, the concept of diagonalization is pivotal for simplifying complex matrix operations. To understand diagonalization, we first need to grasp what a matrix is. A matrix is essentially a rectangular array of numbers arranged in rows and columns, which can represent various types of data and mathematical relationships. The process of diagonalization transforms a given square matrix into a diagonal form, making it significantly easier to compute powers of the matrix and solve systems of linear equations.The significance of diagonalization lies in its ability to simplify matrix operations. When a matrix is diagonalized, it is expressed in the form of D = P^(-1)AP, where D is a diagonal matrix, P is an invertible matrix composed of the eigenvectors of A, and A is the original matrix. This transformation is crucial because diagonal matrices are straightforward to work with; the entries on the diagonal can be manipulated independently, which is not the case with non-diagonal matrices.To achieve diagonalization, several conditions must be met. Firstly, the matrix must be square, meaning it has the same number of rows and columns. Secondly, the matrix must have enough linearly independent eigenvectors to form the matrix P. If these conditions are satisfied, the matrix can be successfully diagonalized.One of the most practical applications of diagonalization is in solving differential equations. Many physical systems can be modeled using differential equations, and diagonalization allows us to find solutions more easily. By transforming the system into a diagonal form, we can decouple the equations, making them simpler to solve individually.Moreover, diagonalization plays a crucial role in various fields such as physics, computer science, and economics. For instance, in quantum mechanics, operators are often represented by matrices, and their diagonalization helps in finding observable quantities. In computer graphics, transformations applied to objects are frequently represented using matrices, and diagonalization can optimize these transformations for rendering.In conclusion, the process of diagonalization is a fundamental technique in linear algebra that simplifies the manipulation of matrices. By converting a matrix into its diagonal form, we gain significant advantages in terms of computational efficiency and ease of solving mathematical problems. Understanding diagonalization not only enhances our grasp of linear algebra but also equips us with powerful tools applicable across various scientific disciplines. As we continue to explore the vast landscape of mathematics, the importance of concepts like diagonalization cannot be overstated, as they serve as the foundation for more advanced theories and applications.

在线性代数领域，对角化的概念对于简化复杂的矩阵运算至关重要。要理解对角化，我们首先需要掌握什么是矩阵。矩阵本质上是一个按行和列排列的数字的矩形数组，可以表示各种类型的数据和数学关系。对角化的过程将给定的方阵转换为对角形式，从而使计算矩阵的幂和求解线性方程组变得更加简单。对角化的重要性在于它能够简化矩阵运算。当一个矩阵被对角化时，它被表示为D = P^(-1)AP，其中D是对角矩阵，P是由A的特征向量组成的可逆矩阵，A是原始矩阵。这种变换至关重要，因为对角矩阵相对容易处理；对角上的条目可以独立操作，而这在非对角矩阵中则无法做到。要实现对角化，必须满足几个条件。首先，矩阵必须是方阵，这意味着它的行数和列数相同。其次，矩阵必须具有足够的线性独立特征向量以形成矩阵P。如果这些条件得到满足，则矩阵可以成功地对角化。对角化的一个最实际的应用是在求解微分方程中。许多物理系统可以用微分方程建模，而对角化使我们更容易找到解决方案。通过将系统转化为对角形式，我们可以将方程解耦，使它们更容易单独求解。此外，对角化在物理学、计算机科学和经济学等多个领域发挥着关键作用。例如，在量子力学中，算子通常用矩阵表示，而它们的对角化有助于找到可观测量。在计算机图形学中，施加于对象的变换通常用矩阵表示，而对角化可以优化这些变换以进行渲染。总之，对角化的过程是线性代数中的一种基本技术，简化了矩阵的操作。通过将矩阵转换为其对角形式，我们在计算效率和解决数学问题的便利性方面获得了显著优势。理解对角化不仅增强了我们对线性代数的掌握，还为我们提供了适用于各个科学学科的强大工具。当我们继续探索数学的广阔领域时，像对角化这样的概念的重要性不容小觑，因为它们构成了更高级理论和应用的基础。