R 简明教程

R - Matrices

矩阵是 R 对象，其中元素按二维矩形布局排列。它们包含相同原子类型的元素。虽然我们可以创建一个只包含字符或只包含逻辑值的矩阵，但它们并没有多大用处。我们使用包含数字元素的矩阵用于数学计算。

Matrices are the R objects in which the elements are arranged in a two-dimensional rectangular layout. They contain elements of the same atomic types. Though we can create a matrix containing only characters or only logical values, they are not of much use. We use matrices containing numeric elements to be used in mathematical calculations.

使用 matrix() 函数创建矩阵。

A Matrix is created using the matrix() function.

Syntax

在 R 中创建矩阵的基本语法为：

The basic syntax for creating a matrix in R is −

matrix(data, nrow, ncol, byrow, dimnames)

以下是所用参数的描述 -

Following is the description of the parameters used −

  1. data is the input vector which becomes the data elements of the matrix.

  2. nrow is the number of rows to be created.

  3. ncol is the number of columns to be created.

  4. byrow is a logical clue. If TRUE then the input vector elements are arranged by row.

  5. dimname is the names assigned to the rows and columns.

Example

创建一个以数字向量为输入的矩阵。

Create a matrix taking a vector of numbers as input.

# Elements are arranged sequentially by row.
M <- matrix(c(3:14), nrow = 4, byrow = TRUE)
print(M)

# Elements are arranged sequentially by column.
N <- matrix(c(3:14), nrow = 4, byrow = FALSE)
print(N)

# Define the column and row names.
rownames = c("row1", "row2", "row3", "row4")
colnames = c("col1", "col2", "col3")

P <- matrix(c(3:14), nrow = 4, byrow = TRUE, dimnames = list(rownames, colnames))
print(P)

当我们执行上述代码时，会产生以下结果 -

When we execute the above code, it produces the following result −

     [,1] [,2] [,3]
[1,]    3    4    5
[2,]    6    7    8
[3,]    9   10   11
[4,]   12   13   14
     [,1] [,2] [,3]
[1,]    3    7   11
[2,]    4    8   12
[3,]    5    9   13
[4,]    6   10   14
     col1 col2 col3
row1    3    4    5
row2    6    7    8
row3    9   10   11
row4   12   13   14

Accessing Elements of a Matrix

矩阵的元素可以通过使用该元素的列和行索引进行访问。我们考虑上面的矩阵 P 来找到下面的特定元素。

Elements of a matrix can be accessed by using the column and row index of the element. We consider the matrix P above to find the specific elements below.

# Define the column and row names.
rownames = c("row1", "row2", "row3", "row4")
colnames = c("col1", "col2", "col3")

# Create the matrix.
P <- matrix(c(3:14), nrow = 4, byrow = TRUE, dimnames = list(rownames, colnames))

# Access the element at 3rd column and 1st row.
print(P[1,3])

# Access the element at 2nd column and 4th row.
print(P[4,2])

# Access only the  2nd row.
print(P[2,])

# Access only the 3rd column.
print(P[,3])

当我们执行上述代码时，会产生以下结果 -

When we execute the above code, it produces the following result −

[1] 5
[1] 13
col1 col2 col3
   6    7    8
row1 row2 row3 row4
   5    8   11   14

Matrix Computations

使用 R 运算符对矩阵执行各种数学运算。运算的结果也是一个矩阵。

Various mathematical operations are performed on the matrices using the R operators. The result of the operation is also a matrix.

参与运算的矩阵的维度（行数和列数）应相同。

The dimensions (number of rows and columns) should be same for the matrices involved in the operation.

Matrix Addition & Subtraction

# Create two 2x3 matrices.
matrix1 <- matrix(c(3, 9, -1, 4, 2, 6), nrow = 2)
print(matrix1)

matrix2 <- matrix(c(5, 2, 0, 9, 3, 4), nrow = 2)
print(matrix2)

# Add the matrices.
result <- matrix1 + matrix2
cat("Result of addition","\n")
print(result)

# Subtract the matrices
result <- matrix1 - matrix2
cat("Result of subtraction","\n")
print(result)

当我们执行上述代码时，会产生以下结果 -

When we execute the above code, it produces the following result −

     [,1] [,2] [,3]
[1,]    3   -1    2
[2,]    9    4    6
     [,1] [,2] [,3]
[1,]    5    0    3
[2,]    2    9    4
Result of addition
     [,1] [,2] [,3]
[1,]    8   -1    5
[2,]   11   13   10
Result of subtraction
     [,1] [,2] [,3]
[1,]   -2   -1   -1
[2,]    7   -5    2

Matrix Multiplication & Division

# Create two 2x3 matrices.
matrix1 <- matrix(c(3, 9, -1, 4, 2, 6), nrow = 2)
print(matrix1)

matrix2 <- matrix(c(5, 2, 0, 9, 3, 4), nrow = 2)
print(matrix2)

# Multiply the matrices.
result <- matrix1 * matrix2
cat("Result of multiplication","\n")
print(result)

# Divide the matrices
result <- matrix1 / matrix2
cat("Result of division","\n")
print(result)

当我们执行上述代码时，会产生以下结果 -

When we execute the above code, it produces the following result −

     [,1] [,2] [,3]
[1,]    3   -1    2
[2,]    9    4    6
     [,1] [,2] [,3]
[1,]    5    0    3
[2,]    2    9    4
Result of multiplication
     [,1] [,2] [,3]
[1,]   15    0    6
[2,]   18   36   24
Result of division
     [,1]      [,2]      [,3]
[1,]  0.6      -Inf 0.6666667
[2,]  4.5 0.4444444 1.5000000