越览(50)——Matlab入门学习(5)之向量运算

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“越览（50）——Matlab入门学习（5）

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“Yue Lan (50)——Matlab introductory

learning (5): Vector operation”

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一、内容摘要（Summary of Content）

本次推文将从内容摘要、思维导图、入门学习来介绍Matlab入门学习（5）之向量运算。

This tweet will introduce the vector operation of Matlab introductory learning (5) from content summary, mind map, and introductory learning.

二、思维导图（Mind Maping）

三、入门学习（introductory learning）

（一）基本概念（Basic concept）

在MATLAB中，向量是一种一维数组，用于存储一系列数值或数据元素。向量可以表示为行向量或列向量，其中行向量是在一行中排列的数据元素，而列向量是在一列中排列的数据元素。

In MATLAB, a vector is a one-dimensional array used to store a series of numerical values or data elements. Vectors can be represented as either row vectors or column vectors, where row vectors are data elements arranged in a row and column vectors are data elements arranged in a column.

向量在MATLAB中通过方括号 [ ] 创建，并用逗号 , 或分号 ;分隔元素来区分行和列。向量支持各种运算，包括加法、减法、标量乘法、点积等，这些运算在MATLAB中可以通过标准的数学运算符简便地执行。向量是MATLAB中处理线性代数、数据分析和算法实现等任务的基础工具之一。

Vectors are created in MATLAB by square brackets [] and separated by commas, or semicolons; elements to distinguish rows and columns. Vectors support a variety of operations, including addition, subtraction, scalar multiplication, dot products, etc. These operations can be easily performed in MATLAB through standard mathematical operators. Vectors are one of the foundational tools in MATLAB for handling tasks such as linear algebra, data analytics, and algorithm implementation.

（二）向量的创建（Vector creation）

在Matlab中，向量的创建有直接输入法、冒号法和利用函数创建的三种方法。

In Matlab, there are three methods for creating vectors: direct input method, colon method and function creation.

1. 直接输入法（Direct input method）

直接输入法就是在命令窗口中直接输入向量。向量元素要用“[]”括起来，元素之间可以用空格、逗号或分号分隔。其中用空格和逗号分隔生成行向量，用分号分隔形成列向量。示例代码如下：

The direct input method is to enter vectors directly in the command window. The elements of the vector should be enclosed by "[]", and the elements can be separated by spaces, commas or semicolons. The row vector is generated by separating spaces and commas, and the column vector is formed by separating semicolons. The example code is as follows:

运行结果如下所示：

The running result is as follows:

2. 冒号法（Colon method）

使用冒号法创建向量，基本格式是“x=first: increment: last”，表示创建一个从first开始，到last结束，每次数据元素增量为increment的向量。若增量为1，创建向量的方式可以简写成“x=first: last”。示例代码如下：

Use the colon method to create a vector. The basic format is "x = first: increment: last", which means to create a vector that starts from first and ends at last, and increments the data elements to increment each time. If the increment is 1, the way to create the vector can be abbreviated as "x = first: last". The example code is as follows:

运行结果如下图所示：

The running result is shown as follows:

3. 利用函数创建向量（Create vectors with functions）

（1）利用函数linspace创建向量（Using function linspace to create vectors）

linspace通过直接定义数据元素，而不是数据元素直接的增量来创建向量。y=linspace(x1,x2)表示创建一个从x1开始，到x2结束，100个等间距的点组成的行向量y。y=linspace(x1,x2，n)表示创建一个从x1开始，到x2结束，等间距的n个元素组成的行向量y。示例代码如下：

A linspace creates a vector by directly defining data elements, rather than direct increments of data elements. y = linspace (x1, x2) means creating a row vector y of 100 equally spaced points starting at x1 and ending at x2. y = linspace (x1, x2, n) means creating a row vector y of n equally spaced elements starting at x1 and ending at x2. The example code is as follows:

运行结果如下所示：

The running result is as follows:

（2）利用函数logspace创建向量（Create vectors with function logspace）

与linspace一样，logspace也通过直接定义向量元素个数，而不是数据元素之间的增量来创建数组。

Like linspaces, logspaces create arrays by directly defining the number of vector elements, rather than increments between data elements.

y=logspace(a,b)表示创建一个从10的a此方开始，到10的b此方结束的50个对数间距点组成的行向量y。y=logspace(a,b,n) 表示创建一个从10的a此方开始，到10的b此方结束的n个对数间距点组成的行向量y。

Y = logspace (a, b) means to create a row vector y of 50 logarithmically spaced points starting at a of 10 and ending at b of 10. y = logspace (a, b, n) means to create a row vector y of n logarithmically spaced points starting at a of 10 and ending at b of 10.

y=logspace(a,pi) 表示创建一个从10的a此方开始，到pi结束的50个对数间距点组成的行向量y。y=logspace(a,pi,n)表示创建一个从10的a此方开始，到pi结束的n个对数间距点组成的行向量y。

Y = logspace (a, pi) means to create a row vector y of 50 logarithmically spaced points starting at a of 10 and ending at pi. Y = logspace (a, pi, n) means to create a row vector y of n logarithmically spaced points starting at a of 10 and ending at pi.

示例代码如下：

The example code is as follows:

运行结果如下图所示：

The running result is shown as follows:

（三）向量运算（Vector operation）

1. 向量的点积运算（Dot Product Operation of Vectors）

在MATLAB中，向量的点积也称为内积或标量积，它是一个重要的线性代数概念。点积的结果是一个标量值，计算方法是将两个向量对应的元素相乘后求和。对于向量a、b，其点积可以通过a’*b得到，或者用命令dot算出。示例代码如下：

In MATLAB, the dot product of a vector is also known as the inner product or scalar product, and it is an important linear algebra concept. The result of the dot product is a scalar value, which is calculated by multiplying and summing the elements corresponding to two vectors. For vectors a and b, the dot product can be obtained by a '* b, or by using the command dot. The example code is as follows:

运行结果如下所示：

The running result is as follows:

2.向量的叉积运算（Vector cross product operation）

向量的叉积是一种特殊的向量运算，它只适用于三维空间中的两个向量。叉积的结果是一个新的向量，该向量垂直于原来的两个向量，并且其长度表示原来两个向量之间形成的平行四边形的面积。

The cross product of a vector is a special vector operation that applies only to two vectors in three-dimensional space. The result of the cross product is a new vector that is perpendicular to the original two vectors and whose length represents the area of the parallelogram formed between the original two vectors.

向量的叉积运算可以用函数cross来实现。cross(a,b)表示返回向量a和b的叉积，不过a和b必须是三维向量。cross(a,b,dim)表示向量a和b在dim维的叉积，其中a和b必须有相同的位数。实例代码如下：

The cross product operation of a vector can be implemented with the function cross. Cross (a, b) represents the cross product that returns vectors a and b, but a and b must be three-dimensional vectors. Cross (a, b, dim) represents the cross product of vectors a and b in the dim dimension, where a and b must have the same number of digits. The example code is as follows:

运行结果如下图所示：

The running result is shown as follows:

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