# Statistical Analysis: an Introduction using R/R/Matrices

Much statistical theory uses matrix algebra. While this book does not require a detailed understanding of matrices, it is useful to know a little about how R handles them.

Input:Essentially, a **matrix** (plural: matrices) is the two dimensional equivalent of a vector. In other words, it is a rectangular grid of numbers, arranged in rows and columns. In R, a matrix object can be created by the `matrix()`

function, which takes, as a first argument, a vector of numbers with which the matrix is filled, and as the second and third arguments, the number of rows and the number of columns respectively.

R can also use **array** objects, which are like matrices, but can have more than 2 dimensions. These are particularly useful for **tables**: a type of array containing counts of data classified according to various criteria. Examples of these "contingency tables" are the `HairEyeColor`

and `Titanic`

tables shown below.

`[]`

can be used to access individual elements or sets of elements in a matrix or array. This is done by separating the numbers inside the brackets by commas. For example, for matrices, you need to specify the row index then a comma, then the column index. If the row index is blank, it is assumed that you want all the rows, and similarly for the columns.```
m <- matrix(1:12, 3, 4) #Create a 3x4 matrix filled with numbers 1 to 12
m #Display it!
m*2 #Arithmetic, just like with vectors
m[2,3] #Pick out a single element (2nd row, 3rd column)
m[1:2, 2:4] #Or a range (rows 1 and 2, columns 2, 3, and 4.)
m[,1] #If the row index is missing, assume all rows
m[1,] #Same for columns
m[,2] <- 99 #You can assign values to one or more elements
m #See!
###Some real data, stored as "arrays"
HairEyeColor #A 3D array
HairEyeColor[,,1] #Select only the males to make it a 2D matrix
Titanic #A 4D array
Titanic[1:3,"Male","Adult",] #A matrix of only the adult male passengers
```

> m <- matrix(1:12, 3, 4) #Create a 3x4 matrix filled with numbers 1 to 12 > m #Display it! [,1] [,2] [,3] [,4] [1,] 1 4 7 10 [2,] 2 5 8 11 [3,] 3 6 9 12 > m*2 #Arithmetic, just like with vectors [,1] [,2] [,3] [,4] [1,] 2 8 14 20 [2,] 4 10 16 22 [3,] 6 12 18 24 > m[2,3] #Pick out a single element (2nd row, 3rd column) [1] 8 > m[1:2, 2:4] #Or a range (rows 1 and 2, columns 2, 3, and 4.) [,1] [,2] [,3] [1,] 4 7 10 [2,] 5 8 11 > m[,1] #If the row index is missing, assume all rows [1] 1 2 3 > m[1,] #Same for columns [1] 1 4 7 10 > m[,2] <- 99 #You can assign values to one or more elements > m #See! [,1] [,2] [,3] [,4] [1,] 1 99 7 10 [2,] 2 99 8 11 [3,] 3 99 9 12 > ###Some real data, stored as "arrays" > HairEyeColor #A 3D array , , Sex = Male Eye Hair Brown Blue Hazel Green Black 32 11 10 3 Brown 53 50 25 15 Red 10 10 7 7 Blond 3 30 5 8 , , Sex = Female Eye Hair Brown Blue Hazel Green Black 36 9 5 2 Brown 66 34 29 14 Red 16 7 7 7 Blond 4 64 5 8 > HairEyeColor[,,1] #Select only the males to make it a 2D matrix Eye Hair Brown Blue Hazel Green Black 32 11 10 3 Brown 53 50 25 15 Red 10 10 7 7 Blond 3 30 5 8 > Titanic #A 4D array , , Age = Child, Survived = No Sex Class Male Female 1st 0 0 2nd 0 0 3rd 35 17 Crew 0 0 , , Age = Adult, Survived = No Sex Class Male Female 1st 118 4 2nd 154 13 3rd 387 89 Crew 670 3 , , Age = Child, Survived = Yes Sex Class Male Female 1st 5 1 2nd 11 13 3rd 13 14 Crew 0 0 , , Age = Adult, Survived = Yes Sex Class Male Female 1st 57 140 2nd 14 80 3rd 75 76 Crew 192 20 > Titanic[1:3,"Male","Adult",] #A matrix of only the adult male passengers Survived Class No Yes 1st 118 57 2nd 154 14 3rd 387 75