如何使用R进行矩阵计算？

Question

我有一个矩阵计算，需要使用R来计算。

Answer 1

z <- matrix(1:9,nrow = 3,byrow = TRUE)
z
     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    4    5    6
[3,]    7    8    9

t(z)%*%z
     [,1] [,2] [,3]
[1,]   66   78   90
[2,]   78   93  108
[3,]   90  108  126

Answer 2

尝试一下：

z<-matrix(seq(1:9),ncol=3,nrow=3,byrow=TRUE)
A=z[1,]*t(z[1,])+z[2,]*t(z[2,])+z[3,]*t(z[3,])
A
#       [,1] [,2] [,3]
#  [1,]   66   93  126

Edit1：以下代码适用于任何尺寸，只要它是方形矩阵即可：

colSums(t(apply(z,1,function(x)(x[1:nrow(z)]*t(x[1:nrow(z)])))))
#[1]  66  93 126

Edit2：

t(z)%*%z #the following 3 lines will all give you the same thing!
crossprod(z) 
matrix(colSums(t(apply(z,1,
function(x)(matrix(x[1:nrow(z)])%*% x[1:nrow(z)])))),ncol=nrow(z),byrow = TRUE)
  #     [,1] [,2] [,3]
 #[1,]   66   78   90
 #[2,]   78   93  108
 #[3,]   90  108  126

Answer 3

尝试一下（使用矩阵乘法）：

library(optimbase)
Z <- matrix(1:9, byrow = TRUE, nrow = 3)
A <- transpose(Z[1, ]) %*% Z[1, ] + transpose(Z[2, ]) %*% Z[2, ] + transpose(Z[3, ]) %*% Z[3, ]
A # output
     [,1] [,2] [,3]
[1,]   66   78   90
[2,]   78   93  108
[3,]   90  108  126

Answer 4

尝试一下：

> z <- matrix(c(1,2,3,4,5,6,7,8,9), 3, byrow=TRUE)
> z
     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    4    5    6
[3,]    7    8    9

> z[1,]
[1] 1 2 3

> matrix(z[1,])
     [,1]
[1,]    1
[2,]    2
[3,]    3

矩阵乘法（列向量*行向量）：

> matrix(z[1,]) %*% z[1,] + matrix(z[2,]) %*% z[2,] + matrix(z[3,]) %*% z[3,]
     [,1] [,2] [,3]
[1,]   66   78   90
[2,]   78   93  108
[3,]   90  108  126

请参阅： http://www.philender.com/courses/multivariate/notes/matr.html

计算行向量*列向量时的结果不同：

> z[1,] %*% matrix(z[1,]) + z[2,] %*% matrix(z[2,]) + z[3,] %*% matrix(z[3,])
     [,1]
[1,]  285