matrix of coefficient

简明释义

系数矩阵

英英释义

例句

1.In machine learning, the optimization algorithm adjusts the matrix of coefficient 系数矩阵 to minimize error.

在机器学习中，优化算法调整 系数矩阵 matrix of coefficient 以最小化误差。

2.To solve the system of equations, we need to find the matrix of coefficient 系数矩阵 first.

要解决方程组，我们首先需要找到 系数矩阵 matrix of coefficient。

3.The matrix of coefficient 系数矩阵 is essential for calculating predictions in multivariate statistics.

在多元统计中，系数矩阵 matrix of coefficient 对于计算预测是必不可少的。

4.In linear regression analysis, the matrix of coefficient 系数矩阵 represents the relationship between independent and dependent variables.

在线性回归分析中，系数矩阵 matrix of coefficient 表示自变量和因变量之间的关系。

5.The matrix of coefficient 系数矩阵 can be derived from the data set using statistical software.

可以使用统计软件从数据集中导出 系数矩阵 matrix of coefficient。

作文

In the realm of mathematics and engineering, the term matrix of coefficient refers to a rectangular array of numbers or symbols that are used to represent the coefficients in a system of linear equations. This concept is fundamental in various fields, such as physics, computer science, and economics, where systems of equations need to be solved to find unknown variables. The matrix of coefficient plays a critical role in simplifying complex problems by allowing us to manipulate multiple equations simultaneously.To illustrate the importance of a matrix of coefficient, let us consider a simple example involving two equations:1. 2x + 3y = 52. 4x - y = 1To express this system in matrix form, we first identify the coefficients of the variables x and y. The coefficients for the first equation are 2 and 3, while for the second equation, they are 4 and -1. We can then create the matrix of coefficient as follows:| 2 3 || 4 -1 |This matrix of coefficient allows us to represent the system of equations compactly. Additionally, we can also represent the constants from the right-hand side of the equations as another matrix:| 5 || 1 |Now, we have converted our system of equations into a matrix equation, which can be solved using various methods such as Gaussian elimination or matrix inversion. This transformation not only simplifies calculations but also provides a clearer visual representation of the relationships between the variables.The utility of the matrix of coefficient extends beyond mere calculations. In advanced applications, such as machine learning and data analysis, matrices are used to represent data sets and perform operations that lead to insights and predictions. For instance, when training a machine learning model, the features of the data can be organized into a matrix of coefficient, enabling algorithms to process and learn patterns effectively.Moreover, the concept of a matrix of coefficient is crucial in understanding concepts like eigenvalues and eigenvectors, which have applications in stability analysis, quantum mechanics, and even population dynamics. By analyzing the matrix of coefficient, researchers can gain insights into the behavior of complex systems.In conclusion, the matrix of coefficient is an essential tool in mathematics and its applications across various disciplines. Its ability to condense information and facilitate calculations makes it invaluable for solving systems of equations and analyzing data. As we continue to explore the depths of mathematics and its applications, a strong grasp of the matrix of coefficient will undoubtedly enhance our problem-solving capabilities and expand our understanding of the world around us.

在数学和工程领域，术语矩阵的系数指的是一个数字或符号的矩形数组，用于表示线性方程组中的系数。这个概念在物理、计算机科学和经济学等多个领域中都是基础，因为这些地方需要解决方程组以找到未知变量。矩阵的系数在通过允许我们同时操纵多个方程来简化复杂问题方面发挥着关键作用。为了说明矩阵的系数的重要性，让我们考虑一个涉及两个方程的简单例子：1. 2x + 3y = 52. 4x - y = 1要将这个系统表示为矩阵形式，我们首先确定变量x和y的系数。第一个方程的系数是2和3，而第二个方程的系数是4和-1。我们可以如下创建矩阵的系数：| 2 3 || 4 -1 |这个矩阵的系数使我们能够紧凑地表示方程组。此外，我们还可以将方程右侧的常数表示为另一个矩阵：| 5 || 1 |现在，我们已经将方程组转换为矩阵方程，这可以通过高斯消元法或矩阵逆运算等各种方法进行求解。这种变换不仅简化了计算，还提供了变量之间关系的更清晰的视觉表示。矩阵的系数的实用性不仅限于简单的计算。在机器学习和数据分析等高级应用中，矩阵用于表示数据集并执行操作，从而得出见解和预测。例如，在训练机器学习模型时，数据的特征可以组织成矩阵的系数，使算法能够有效地处理和学习模式。此外，矩阵的系数的概念对于理解特征值和特征向量等概念至关重要，这些概念在稳定性分析、量子力学甚至种群动态中都有应用。通过分析矩阵的系数，研究人员可以获得对复杂系统行为的洞察。总之，矩阵的系数是数学及其在各个学科应用中的重要工具。它能够浓缩信息并促进计算，使其在解决方程组和分析数据时不可或缺。随着我们继续探索数学及其应用的深度，对矩阵的系数的深入理解无疑将增强我们的解决问题能力，并扩展我们对周围世界的理解。