1 Vectors

A vector contains homogeneous data type and it is 1-dimensional.

For example:

vec1 = c(1, 2, 4, 8, 16)
vec1

[1]  1  2  4  8 16

vec2 = c("a", "b", "c")
vec2

[1] "a" "b" "c"

2 Matrices

A matrix contains homogeneous data type and it has 1 or 2 dimensions. It has rows and columns that are numbered or can be named.

For example:

mat1 = matrix(c(1, 2, 4, 8, 
                16, 32, 64, 128,
                256, 512, 1024, 2048),
              nrow = 3, byrow = TRUE)
mat1

     [,1] [,2] [,3] [,4]
[1,]    1    2    4    8
[2,]   16   32   64  128
[3,]  256  512 1024 2048

mat2 = matrix(c(c("a", "b", "c"), 
                c("x", "y", "z")), 
              ncol = 2, byrow = FALSE)
# Name the rows and columns
rownames(mat2) = c("A1", "A2", "A3")
colnames(mat2) = c("B1", "B2")
mat2

   B1  B2 
A1 "a" "x"
A2 "b" "y"
A3 "c" "z"

3 Arrays

An array contains homogeneous data type and it can have 1 or more dimensions. Its dimensions are numbered or can be named.

Create a 3 dimensional array:

arr1 = array(c("a", "b", "c", "d", "e", "f", 
               "g", "h", "i", "j", "k", "l"),
             dim = c(2, 3, 2))
arr1

, , 1

     [,1] [,2] [,3]
[1,] "a"  "c"  "e" 
[2,] "b"  "d"  "f" 

, , 2

     [,1] [,2] [,3]
[1,] "g"  "i"  "k" 
[2,] "h"  "j"  "l" 

# Name the rows and columns
colnames(arr1) = c("A1", "A2", "A3")
rownames(arr1) = c("B1", "B2")
arr1

, , 1

   A1  A2  A3 
B1 "a" "c" "e"
B2 "b" "d" "f"

, , 2

   A1  A2  A3 
B1 "g" "i" "k"
B2 "h" "j" "l"

Create a 4 dimensional array:

arr2 = array(c(1, 2, 4, 8,
               16, 32, 64, 128,
               256, 512, 1024, 2048,
               4096, 8192, 16384, 32768),
             dim = c(2, 2, 2, 2))
arr2

, , 1, 1

     [,1] [,2]
[1,]    1    4
[2,]    2    8

, , 2, 1

     [,1] [,2]
[1,]   16   64
[2,]   32  128

, , 1, 2

     [,1] [,2]
[1,]  256 1024
[2,]  512 2048

, , 2, 2

     [,1]  [,2]
[1,] 4096 16384
[2,] 8192 32768

4 Dataframes

A dataframe can contain homogeneous or heterogeneous data types, it is 2-dimensional with rows and columns that are numbered or can be named.

dtfrm1 = data.frame(Team = c("A", "B", "B", "C", "D"), 
                   Score = c(9, 8, 8, 10, 7), 
                   Position = c(2, 3, 3, 1, 5))
dtfrm1

  Team Score Position
1    A     9        2
2    B     8        3
3    B     8        3
4    C    10        1
5    D     7        5

# Name the rows
rownames(dtfrm1) = c("R1", "R2", "R3", "R4", "R5")
dtfrm1

   Team Score Position
R1    A     9        2
R2    B     8        3
R3    B     8        3
R4    C    10        1
R5    D     7        5

5 Lists

A list can contain homogeneous or heterogeneous data types which includes vectors, matrices, arrays, dataframes and other lists (or list of lists). It can have 1 or more levels with each level numbered or can be named.

ls1 = list(vec1, mat1, "array" = arr1, "dataframe" = dtfrm1)
ls1

[[1]]
[1]  1  2  4  8 16

[[2]]
     [,1] [,2] [,3] [,4]
[1,]    1    2    4    8
[2,]   16   32   64  128
[3,]  256  512 1024 2048

$array
, , 1

   A1  A2  A3 
B1 "a" "c" "e"
B2 "b" "d" "f"

, , 2

   A1  A2  A3 
B1 "g" "i" "k"
B2 "h" "j" "l"


$dataframe
   Team Score Position
R1    A     9        2
R2    B     8        3
R3    B     8        3
R4    C    10        1
R5    D     7        5