## 1.1 Creating matrices in R

Create a $$3 \times 4$$ matrix, meaning 3 row and 4 columns, that is all 1s:

matrix(1, 3, 4)
     [,1] [,2] [,3] [,4]
[1,]    1    1    1    1
[2,]    1    1    1    1
[3,]    1    1    1    1

Create a $$3 \times 4$$ matrix filled in with the numbers 1 to 12 by column (default) and by row:

matrix(1:12, 3, 4)
     [,1] [,2] [,3] [,4]
[1,]    1    4    7   10
[2,]    2    5    8   11
[3,]    3    6    9   12
matrix(1:12, 3, 4, byrow = TRUE)
     [,1] [,2] [,3] [,4]
[1,]    1    2    3    4
[2,]    5    6    7    8
[3,]    9   10   11   12

Create a matrix with one column:

matrix(1:4, ncol = 1)
     [,1]
[1,]    1
[2,]    2
[3,]    3
[4,]    4

Create a matrix with one row:

matrix(1:4, nrow = 1)
     [,1] [,2] [,3] [,4]
[1,]    1    2    3    4

Check the dimensions of a matrix

A = matrix(1:6, 2, 3)
A
     [,1] [,2] [,3]
[1,]    1    3    5
[2,]    2    4    6
dim(A)
[1] 2 3

Get the number of rows in a matrix:

dim(A)[1]
[1] 2
nrow(A)
[1] 2

Create a 3D matrix (called array):

A = array(1:6, dim = c(2, 3, 2))
A
, , 1

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

, , 2

[,1] [,2] [,3]
[1,]    1    3    5
[2,]    2    4    6
dim(A)
[1] 2 3 2

Check if an object is a matrix. A data frame is not a matrix. A vector is not a matrix.

A = matrix(1:4, 1, 4)
A
     [,1] [,2] [,3] [,4]
[1,]    1    2    3    4
class(A)
[1] "matrix" "array" 
B = data.frame(A)
B
  X1 X2 X3 X4
1  1  2  3  4
class(B)
[1] "data.frame"
C = 1:4
C
[1] 1 2 3 4
class(C)
[1] "integer"