矩陣的存儲默認是按列進行存儲的
1,創建矩陣
matrix (data = NA, nrow = 1, ncol = 1, byrow =FALSE, dimnames = NULL)
創建一個c(1:12)的三行四列的矩陣,
colnames<-c("c1","c2","c3","c4")
rownames<-c("r1","r2","r3")
x<-matrix(1:12,nrow=3,ncol=4,byrow=TRUE,dimnames=list(rownames,colnames))
x
c1 c2 c3 c4
r1 1 2 3 4
r2 5 6 7 8
r3 9 10 11 12
2,矩陣的轉置
y<-t(x)
若是針對的是一個向量
y<-(1:10)
裝置后得到的是行向量
> t(y)
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 1 2 3 4 5 6 7 8 9 10
> class(y)
[1] "integer"
> class(t(y))
[1] "matrix"
若要的到列向量則
> t(t(y))
[,1]
[1,] 1
[2,] 2
[3,] 3
[4,] 4
[5,] 5
[6,] 6
[7,] 7
[8,] 8
[9,] 9
[10,] 10
3,創建一個服從正態分布的隨機數矩陣
matrix(rnorm(100),nrow=10)
4,制造一個數字相同的n列m行矩陣
matrix(2,ncol=n,nrow=m)
4.1創建對角矩陣
diag(x,ncol=n,nrow=m)
若x為矩陣 則diag(x)將會提取矩陣x的對角,則返回的是向量值
> diag(x)
[1] 1 6 11
> diag(diag(x))
[,1] [,2] [,3]
[1,] 1 0 0
[2,] 0 6 0
[3,] 0 0 11
返回的是以矩陣對角的對角矩陣
>diag(c(1:4),4,4)
[,1] [,2] [,3] [,4]
[1,] 1 0 0 0
[2,] 0 2 0 0
[3,] 0 0 3 0
[4,] 0 0 0 4
>diag(3)
[,1] [,2] [,3]
[1,] 1 0 0
[2,] 0 1 0
[3,] 0 0 1
>A=diag(4)+1
> A
[,1] [,2] [,3] [,4]
[1,] 2 1 1 1
[2,] 1 2 1 1
[3,] 1 1 2 1
[4,] 1 1 1 2
4,求矩陣的行數和列數
n<-ncol
m<-nrow
為矩陣的行和列命名
rownames(x)<-c()
colnames(x)<c()
5,矩陣運算
A為m×n矩陣,c>0,在R中求cA可用符號:“*”,例如:
> c=2
> c*A
[,1] [,2] [,3] [,4]
[1,] 2 8 14 20
[2,] 4 10 16 22
[3,] 6 12 18 24
6 矩陣相乘
A為m×n矩陣,B為n×k矩陣,在R中求AB可用符號:“%*%”,例如:
> A=matrix(1:12,nrow=3,ncol=4)
> B=matrix(1:12,nrow=4,ncol=3)
> A%*%B
[,1] [,2] [,3]
[1,] 70 158 246
[2,] 80 184 288
[3,] 90 210 330
對矩陣求逆
solve(x)
7,向量和矩陣的內積和外積運算(向量的長度一樣)
向量的內積
x<-c(1:5)
y<-c(3:7)
> z<-crossprod(x,y)
> z
[,1]
[1,] 85
向量的外積
> w<-tcrossprod(x,y)
> w
[,1] [,2] [,3] [,4] [,5]
[1,] 3 4 5 6 7
[2,] 6 8 10 12 14
[3,] 9 12 15 18 21
[4,] 12 16 20 24 28
[5,] 15 20 25 30 35
向量、矩陣的外積(叉積)
設x和y是n維向量,則x%o%y表示x與y作外積.
> q<-x%o%y
> q
[,1] [,2] [,3] [,4] [,5]
[1,] 3 4 5 6 7
[2,] 6 8 10 12 14
[3,] 9 12 15 18 21
[4,] 12 16 20 24 28
[5,] 15 20 25 30 35
> a %o% b
, , 1, 1
[,1] [,2] [,3] [,4]
[1,] 1 4 7 10
[2,] 2 5 8 11
[3,] 3 6 9 12
, , 2, 1
[,1] [,2] [,3] [,4]
[1,] 2 8 14 20
[2,] 4 10 16 22
[3,] 6 12 18 24
, , 1, 2
[,1] [,2] [,3] [,4]
[1,] 3 12 21 30
[2,] 6 15 24 33
[3,] 9 18 27 36
, , 2, 2
[,1] [,2] [,3] [,4]
[1,] 4 16 28 40
[2,] 8 20 32 44
[3,] 12 24 36 48
outer()是更為強大的外積運算函數,outer(x,y)計算向量x與y的外積,它等價於x %o%y
函數。outer()的一般調用格式為
outer(x,y,fun=”*”)
det(x),求矩陣x的行列式值
qr(x)$rank求x矩陣的秩
解線性方程組和求矩陣的逆矩陣
若求解線性方程組Ax=b,其命令形式為solve(A,b),求矩陣A的逆,其命令形式為solve(A).設矩陣A=t(array(c(1:8,10),dim=c(3,3))),b<-c(1,1,1),則解方程組Ax=b的解x和求矩陣A的逆矩陣的命令如下: