R基础知识-矩阵

矩阵

矩阵内的每个元素都有相同的模式

创建矩阵

matrix(data = NA, nrow = 1, ncol = 1, byrow = FALSE, dimnames = NULL)

as.matrix(x, ...)

## S3 method for class 'data.frame'

as.matrix(x, rownames.force = NA, ...)

is.matrix(x)

> m1 <- matrix(c(1:30), nrow=5, ncol=6, byrow=T, dimnames = list(c("A", "B", "C", "D","E"), c("a", "b", "c", "d", "e", "f")))

> m1

a b c d e f

A 1 2 3 4 5 6

B 7 8 9 10 11 12

C 13 14 15 16 17 18

D 19 20 21 22 23 24

E 25 26 27 28 29 30

> m2 <- matrix(c(1:30), nrow =5, ncol=6, byrow=F, dimnames = list(c("A", "B", "C", "D","E"), c("a", "b", "c", "d", "e", "f")))

> m2

a b c d e f

A 1 6 11 16 21 26

B 2 7 12 17 22 27

C 3 8 13 18 23 28

D 4 9 14 19 24 29

E 5 10 15 20 25 30

默认是按照列排列的，也就是说byrow=FALSE

dim(x):查看变量的维数；重新设置的维数，例如dim(x)=c(3,2)

> dim(m2) = c(6,5)

> m2

[,1] [,2] [,3] [,4] [,5]

[1,] 1 7 13 19 25

[2,] 2 8 14 20 26

[3,] 3 9 15 21 27

[4,] 4 10 16 22 28

[5,] 5 11 17 23 29

[6,] 6 12 18 24 30

> dim(m2)

[1] 6 5

> dim(m2)=c(5,6)

> dim(m2)

[1] 5 6

> m2

[,1] [,2] [,3] [,4] [,5] [,6]

[1,] 1 6 11 16 21 26

[2,] 2 7 12 17 22 27

[3,] 3 8 13 18 23 28

[4,] 4 9 14 19 24 29

[5,] 5 10 15 20 25 30

matrix创建矩阵

dim 查看矩阵维度，重新设置维度

注意这里在定义dimnames时，用的是list

矩阵转化为向量

> x <- c(1:10)

> m3 <- matrix(x, nrow=5, ncol=2, byrow = F)

> m3

[,1] [,2]

[1,] 1 6

[2,] 2 7

[3,] 3 8

[4,] 4 9

[5,] 5 10

> b<- as.vector(m3)

> b

[1] 1 2 3 4 5 6 7 8 9 10

> m3

[,1] [,2]

[1,] 1 6

[2,] 2 7

[3,] 3 8

[4,] 4 9

[5,] 5 10

> m4 <- matrix(x, nrow=5, ncol=2, byrow = T)

> m4

[,1] [,2]

[1,] 1 2

[2,] 3 4

[3,] 5 6

[4,] 7 8

[5,] 9 10

> d <- as.vector(m4)

> d

[1] 1 3 5 7 9 2 4 6 8 10

这里将matrix转换成向量使用as.vector()

矩阵索引

矩阵跟向量类似，使用下标和方括号来访问矩阵中的元素。

x[1,] 访问第一行的所有元素

x[,1] 访问第一列的所有元素

x[i, j] 访问i行 j列的元素

> m2

[,1] [,2] [,3] [,4] [,5] [,6]

[1,] 1 6 11 16 21 26

[2,] 2 7 12 17 22 27

[3,] 3 8 13 18 23 28

[4,] 4 9 14 19 24 29

[5,] 5 10 15 20 25 30

> m2[2,]

[1] 2 7 12 17 22 27

> m2[,3]

[1] 11 12 13 14 15

> m2[3,4]

[1] 18

> m2[c(2:4),]

[,1] [,2] [,3] [,4] [,5] [,6]

[1,] 2 7 12 17 22 27

[2,] 3 8 13 18 23 28

[3,] 4 9 14 19 24 29

> m2[, c(3:5)]

[,1] [,2] [,3]

[1,] 11 16 21

[2,] 12 17 22

[3,] 13 18 23

[4,] 14 19 24

[5,] 15 20 25

矩阵的运算

矩阵的运算比较丰富，包括四则运算，对行求和，对列求和等。

> m2

[,1] [,2] [,3] [,4] [,5] [,6]

[1,] 1 6 11 16 21 26

[2,] 2 7 12 17 22 27

[3,] 3 8 13 18 23 28

[4,] 4 9 14 19 24 29

[5,] 5 10 15 20 25 30

> colSums(m2)

[1] 15 40 65 90 115 140

> rowSums(m2)

[1] 81 87 93 99 105

> colMeans(m2)

[1] 3 8 13 18 23 28

> rowMeans(m2)

[1] 13.5 14.5 15.5 16.5 17.5

> t(m2)

[,1] [,2] [,3] [,4] [,5]

[1,] 1 2 3 4 5

[2,] 6 7 8 9 10

[3,] 11 12 13 14 15

[4,] 16 17 18 19 20

[5,] 21 22 23 24 25

[6,] 26 27 28 29 30

> crossprod(m2)

[,1] [,2] [,3] [,4] [,5] [,6]

[1,] 55 130 205 280 355 430

[2,] 130 330 530 730 930 1130

[3,] 205 530 855 1180 1505 1830

[4,] 280 730 1180 1630 2080 2530

[5,] 355 930 1505 2080 2655 3230

[6,] 430 1130 1830 2530 3230 3930

> m2

[,1] [,2] [,3] [,4] [,5] [,6]

[1,] 1 6 11 16 21 26

[2,] 2 7 12 17 22 27

[3,] 3 8 13 18 23 28

[4,] 4 9 14 19 24 29

[5,] 5 10 15 20 25 30

> t(m2)

[,1] [,2] [,3] [,4] [,5]

[1,] 1 2 3 4 5

[2,] 6 7 8 9 10

[3,] 11 12 13 14 15

[4,] 16 17 18 19 20

[5,] 21 22 23 24 25

[6,] 26 27 28 29 30

> m2%*%t(m2)

[,1] [,2] [,3] [,4] [,5]

[1,] 1531 1612 1693 1774 1855

[2,] 1612 1699 1786 1873 1960

[3,] 1693 1786 1879 1972 2065

[4,] 1774 1873 1972 2071 2170

[5,] 1855 1960 2065 2170 2275

> diag(m2)

[1] 1 7 13 19 25

> solve(m2)

Error in solve.default(m2) : 'a' (5 x 6) must be square

> eigen(m2)

Error in eigen(m2) : eigen里的矩阵不是正方形的

矩阵

矩阵转化为向量

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