矩陣是其中元素以二維矩形布局排列的R對象。它們包含相同原子類型的元素。 雖然我們可以創(chuàng)建一個僅包含字符或僅包含邏輯值的矩陣，但它們沒有太多用處。 我們使用包含數(shù)學(xué)元素的矩陣來在數(shù)學(xué)計算中使用。

矩陣可通過使用matrix()函數(shù)來創(chuàng)建。

語法

在R中創(chuàng)建矩陣的基本語法是 -

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

以下是使用的參數(shù)的描述 -

• data - 是將要轉(zhuǎn)為矩陣元素的輸入向量。
• nrow - 是要創(chuàng)建的行數(shù)。
• ncol - 是要創(chuàng)建的列數(shù)。
• byrow - 是一個邏輯線索。 如果為TRUE，則輸入向量元素按行排列。
• dimname - 是分配給行和列的名稱。

例子

創(chuàng)建一個使用數(shù)字向量作為輸入的矩陣，參考以下代碼 -

# 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)

當(dāng)我們執(zhí)行上述代碼時，會產(chǎn)生以下結(jié)果 -

     [,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

訪問矩陣的元素

可以使用元素的列和行索引來訪問矩陣的元素。 我們考慮上面的矩陣P來找到下面的具體元素。

# 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])

當(dāng)我們執(zhí)行上述代碼時，會產(chǎn)生以下結(jié)果 -

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

矩陣計算

使用R運算符對矩陣執(zhí)行各種數(shù)學(xué)運算，操作的結(jié)果也是一個矩陣。

操作中涉及的矩陣的尺寸(行數(shù)和列數(shù))應(yīng)相同。

矩陣加法與減法運算示例 -

# 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)

當(dāng)我們執(zhí)行上述代碼時，會產(chǎn)生以下結(jié)果 -

     [,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

矩陣乘法與除法運算示例

# 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)

當(dāng)我們執(zhí)行上述代碼時，會產(chǎn)生以下結(jié)果 -

     [,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