\usepackage{amsmath}
There are many different data structure types in R, each with varying levels of complexity and uses. The simplest data structure in R is a vector. Vectors are one-dimensional arrays (i.e., sets of values) of a single class (such as characters, numbers, dates, etc.), and they have a similar structure to the mathematical concept of vectors. For example, the vector $\vec v$ with values 1, 4, 6, 2 would be:
\[\vec v = \begin{bmatrix}1 \\ 4 \\ 6 \\ 2\end{bmatrix}.\]
In R we can create vectors using the c() function, as follows:
(R prints vectors in a line rather than as columns to improve readability.)
Since vectors can only contain elements of a common type, c() will force all elements to be of a single class. In the example below, I create a vector with the number 1, the letter “a”, today’s date, and the value TRUE (a boolean value), but c() coerces all values to be characters:
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| c(1, 'a', Sys.Date(), TRUE)
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| ## [1] "1" "a" "19551" "TRUE"
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If we place two vectors (of the same class) side by side, we can create a matrix. Matrices are thus two-dimensional arrays
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| # 2D arrays: matrices
matrix(data = 1:8, nrow = 2)
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2
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| ## [,1] [,2] [,3] [,4]
## [1,] 1 3 5 7
## [2,] 2 4 6 8
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| matrix(data = 1:8, ncol = 2)
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| ## [,1] [,2]
## [1,] 1 5
## [2,] 2 6
## [3,] 3 7
## [4,] 4 8
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| matrix(data = 1:8, ncol = 2, byrow = TRUE)
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| ## [,1] [,2]
## [1,] 1 2
## [2,] 3 4
## [3,] 5 6
## [4,] 7 8
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| # matrix operations
matrix(1:9, ncol = 3)
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| ## [,1] [,2] [,3]
## [1,] 1 4 7
## [2,] 2 5 8
## [3,] 3 6 9
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| matrix(1:9, ncol = 3) + 3
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| ## [,1] [,2] [,3]
## [1,] 4 7 10
## [2,] 5 8 11
## [3,] 6 9 12
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| matrix(1:9, ncol = 3) * 2 # NOT matrix multiplication
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| ## [,1] [,2] [,3]
## [1,] 2 8 14
## [2,] 4 10 16
## [3,] 6 12 18
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| matrix(1:9, ncol = 3) %*% 6:8 # matrix multiplication
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| ## [,1]
## [1,] 90
## [2,] 111
## [3,] 132
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| matrix(1:9, ncol = 3) %*% matrix(1:6, ncol = 2)
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| ## [,1] [,2]
## [1,] 30 66
## [2,] 36 81
## [3,] 42 96
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| # grouping objects with different and types: lists
l <- list(letters = c('a', 'b', 'c'),
numbers = 1:10,
today = Sys.Date())
l
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| ## $letters
## [1] "a" "b" "c"
##
## $numbers
## [1] 1 2 3 4 5 6 7 8 9 10
##
## $today
## [1] "2023-07-13"
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| # lists with a table-like structure: data frames
#' note: `data.frame()` recycles elements if the longest vector is a multiple
data.frame(numbers = 1:10,
letters = c('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'))
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| ## numbers letters
## 1 1 a
## 2 2 b
## 3 3 c
## 4 4 d
## 5 5 e
## 6 6 f
## 7 7 g
## 8 8 h
## 9 9 i
## 10 10 j
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