颜读（45）：MATLAB入门学习之矩阵运算

摘要：矩阵运算具体包括：矩阵加减法、矩阵乘法、矩阵除法、矩阵幂运算、点运算。其中矩阵的加法和减法要求参与运算的矩阵具有相同的维度（即相同的行数和列数）。矩阵乘法要求第一个矩阵的列数等于第二个矩阵的行数。MATLAB中有两种矩阵除法：左除和右除。除了标准的矩阵运算，M

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一、思维导图（Mind Mapping）

二、矩阵运算（Matrix operations）

矩阵运算具体包括：矩阵加减法、矩阵乘法、矩阵除法、矩阵幂运算、点运算。其中矩阵的加法和减法要求参与运算的矩阵具有相同的维度（即相同的行数和列数）。矩阵乘法要求第一个矩阵的列数等于第二个矩阵的行数。MATLAB中有两种矩阵除法：左除和右除。除了标准的矩阵运算，MATLAB还支持点运算，即对矩阵的每个元素进行运算。点乘（.*）、点除（./）和点幂（.^）都是对应元素进行运算，要求矩阵维度相同。示例如下：

Matrix operations specifically include: matrix addition and subtraction, Matrix multiplication, matrix division, matrix power operation, and dot operation. Matrix addition and subtraction require that the matrices involved in the operation have the same dimensions (that is, the same number of rows and columns). Matrix multiplication requires that the number of columns of the first matrix is equal to the number of rows of the second matrix. There are two types of matrix division in MATLAB: left division and right division. In addition to standard matrix operations, MATLAB also supports dot operations, that is, operations on each element of the matrix. Dot multiplication (.*), dot division (./), and dot power (.^) all operate on corresponding elements and require the matrices to have the same dimensions. The examples are as follows:

三、矩阵元素的计算（Calculation of matrix elements）

（1）mean函数（mean function）

MATLAB中的mean函数用于计算矩阵元素的平均值。若a为矩阵，则mean(a)是按列求平均值，mean(a,2)是按行求平均值。

The mean function in MATLAB is used to calculate the mean of matrix elements. If a is a matrix, mean(a) calculates the mean by column, and mean(a,2) calculates the mean by row.

（2）sum函数（sum function）

MATLAB中的sum函数用于计算矩阵元素的总和。若a为矩阵，则sum(a)是按列求和，sum(a,2)是按行求和。

The sum function in MATLAB is used to calculate the sum of matrix elements. If a is a matrix, then sum(a) sums the columns, and sum(a,2) sums the rows.

四、矩阵元素的比较和排序（Comparing and sorting matrix elements）

（1）max函数（max function）

max函数用于计算矩阵元素的最大值。示例如下：

The max function is used to calculate the maximum value of matrix elements. The following example:

sort函数用于对矩阵元素进行升序排序。示例如下：

The sort function is used to sort matrix elements in ascending order. The following example shows:

（3）sortrows函数（sortrows function）

sortrows函数用于按行对整个矩阵进行排序，基于指定列的值。需要注意的是，当使用sortrows(A)而不指定列时，MATLAB的默认行为是：按第一列排序；当第一列相同时，按第二列排序；当第一列和第二列都相同时，按第三列排序。示例如下：

The sortrows function is used to sort the entire matrix by row, based on the values of the specified column. It should be noted that when using sortrows(A) without specifying a column, MATLAB's default behavior is to sort by the first column; when the first columns are the same, sort by the second column; when the first and second columns are the same, sort by the third column. The following is an example: