# some matrices and vectors
W <- matrix(c(1:4),ncol=3,nrow=2)
## Warning in matrix(c(1:4), ncol = 3, nrow = 2): Datenlänge [4] ist kein
## Teiler oder Vielfaches der Anzahl der Spalten [3]
X <- matrix(c(1:8),ncol=2,nrow=4)
y <- as.matrix(c(1:4))
z <- as.matrix(c(5,6))

Computing with matrices

Addition

z
##      [,1]
## [1,]    5
## [2,]    6
z+z
##      [,1]
## [1,]   10
## [2,]   12
W
##      [,1] [,2] [,3]
## [1,]    1    3    1
## [2,]    2    4    2
W+W
##      [,1] [,2] [,3]
## [1,]    2    6    2
## [2,]    4    8    4

Scalar multiplication

z
##      [,1]
## [1,]    5
## [2,]    6
4*z
##      [,1]
## [1,]   20
## [2,]   24
W
##      [,1] [,2] [,3]
## [1,]    1    3    1
## [2,]    2    4    2
4*W
##      [,1] [,2] [,3]
## [1,]    4   12    4
## [2,]    8   16    8

Component-wise multiplication

z
##      [,1]
## [1,]    5
## [2,]    6
z*z
##      [,1]
## [1,]   25
## [2,]   36
W
##      [,1] [,2] [,3]
## [1,]    1    3    1
## [2,]    2    4    2
W*W
##      [,1] [,2] [,3]
## [1,]    1    9    1
## [2,]    4   16    4

Matrix multiplication

z
##      [,1]
## [1,]    5
## [2,]    6
# z' x z
t(z) %*% z
##      [,1]
## [1,]   61
X
##      [,1] [,2]
## [1,]    1    5
## [2,]    2    6
## [3,]    3    7
## [4,]    4    8
W
##      [,1] [,2] [,3]
## [1,]    1    3    1
## [2,]    2    4    2
# W x X
X %*% W
##      [,1] [,2] [,3]
## [1,]   11   23   11
## [2,]   14   30   14
## [3,]   17   37   17
## [4,]   20   44   20

Transposed matrix

X
##      [,1] [,2]
## [1,]    1    5
## [2,]    2    6
## [3,]    3    7
## [4,]    4    8
# X'
t(X)
##      [,1] [,2] [,3] [,4]
## [1,]    1    2    3    4
## [2,]    5    6    7    8

z’

z
##      [,1]
## [1,]    5
## [2,]    6
# z'
t(z)
##      [,1] [,2]
## [1,]    5    6