Working with matrices in R.

A matrix is a collection of elements of the same data type, with the data being arranged into rows and columns. Because it consists of both rows and columns, matrices are considered two-dimensional as opposed to vectors, which are considered one-dimensional.

DataQuest analyzes university rankings for this lesson. However, for this post, I decided that I would analyze six of the highest-grossing films of all time. The data that I’ll be working with in this post comes from Box Office Mojo. Please note that for the last two columns, Budget in Millions and Domestic Opening in Millions, I rounded the numbers so the values in these columns are not exact.

To create a matrix using the data above, DataQuest taught me that I must first create vectors.

I can easily combine this vectors into a matrix using the function rbind(). The r in rbind() stands for row and this function allows us to combine multiple vectors and matrices by row.

```
film_matrix <-rbind(endgame, avatar, titanic, star_wars, infinity_war, jurassic_world)
film_matrix
```

```
[,1] [,2] [,3] [,4] [,5]
endgame 1 2019 181 356 357
avatar 2 2009 162 237 77
titanic 3 1997 194 200 28
star_wars 4 2015 138 245 248
infinity_war 5 2018 149 316 258
jurassic_world 6 2015 124 150 209
```

I then learned that I could name the rows and columns in a matrix. I could use the functions **rownames()** to name rows and **colnames()** to name columns. First, I stored the names of the columns into a vector called **categories**. I then used the function colnames() to assign those names to the columns in my matrix.

```
categories <- c("rank", "year", "runtime_minutes", "budget_millions", "domestic_opening_millions")
colnames(film_matrix) <-categories
film_matrix
```

```
rank year runtime_minutes budget_millions
endgame 1 2019 181 356
avatar 2 2009 162 237
titanic 3 1997 194 200
star_wars 4 2015 138 245
infinity_war 5 2018 149 316
jurassic_world 6 2015 124 150
domestic_opening_millions
endgame 357
avatar 77
titanic 28
star_wars 248
infinity_war 258
jurassic_world 209
```

If I wanted to identify the dimensions (the number of rows and columns) in a matrix, I would use the **dim()** function. The output of this function gives me two numbers. The first number is the number of rows; the second number is the number of columns.

```
dim(film_matrix)
```

`[1] 6 5`

Earlier in this post, I combined vectors into a matrix using rbind() and it allowed me to combine my vectors by row. The function, **cbind()** allows me to combine vectors and matrices by column.

Let’s say I wanted to add the domestic gross of the films as a column to this matrix. First, I would get the domestic gross of the films. Next, I would use cbind() to add the **domestic_gross_millions** column to the existing matrix.

```
domestic_gross_millions<-c(858, 761, 659, 937, 679, 652)
cbind(film_matrix, domestic_gross_millions)
```

```
rank year runtime_minutes budget_millions
endgame 1 2019 181 356
avatar 2 2009 162 237
titanic 3 1997 194 200
star_wars 4 2015 138 245
infinity_war 5 2018 149 316
jurassic_world 6 2015 124 150
domestic_opening_millions domestic_gross_millions
endgame 357 858
avatar 77 761
titanic 28 659
star_wars 248 937
infinity_war 258 679
jurassic_world 209 652
```

I then stored the result in a new matrix called **entire_matrix**.

```
entire_matrix <- cbind(film_matrix, domestic_gross_millions)
entire_matrix
```

```
rank year runtime_minutes budget_millions
endgame 1 2019 181 356
avatar 2 2009 162 237
titanic 3 1997 194 200
star_wars 4 2015 138 245
infinity_war 5 2018 149 316
jurassic_world 6 2015 124 150
domestic_opening_millions domestic_gross_millions
endgame 357 858
avatar 77 761
titanic 28 659
star_wars 248 937
infinity_war 258 679
jurassic_world 209 652
```

When adding a vector to a matrix, it’s important to make sure that the new vector is the same length as the number of rows and columns in the matrix.

Just as I indexed vectors, I learned that I could also index matrices. Since matrices are two-dimensional, they can be indexed in the following ways:

- index to select specific values

- index to select specific rows and columns

Let’s say I wanted to extract the year that Avengers: Infinity War was released. I have to specify the location of this element by row and and column. In the screenshot below, you can see that Infinity War is in **row 5** and the year is in **column 2**.

```
entire_matrix[5,2]
```

`[1] 2018`

I can also index matrices by row and column names instead of position:

```
entire_matrix["infinity_war", "year"]
```

`[1] 2018`

I can specify the range of columns since the **budget_in_millions** and **domestic_gross_millions** columns are next to each other.

```
entire_matrix[5, 4:5]
```

```
budget_millions domestic_opening_millions
316 258
```

I can also index columns are not next to each other. Let’s say I wanted index elements from the columns **rank** and **runtime_minutes**. Here I index these columns in two ways. The first example is by position, the second example is by name.

```
rank runtime_minutes
titanic 3 194
infinity_war 5 149
```

As mentioned, I can index to select a specific row or column. Let’s say I want to extract all the rankings for Avatar. All the rankings for Avatar are in row 2 of my matrix. I would indicate that I want to index all the elements of row 2 and leave the column position blank.

```
entire_matrix["avatar", ]
```

```
rank year
2 2009
runtime_minutes budget_millions
162 237
domestic_opening_millions domestic_gross_millions
77 761
```

When I write an expression to index an entire row or column, I only need to specify the name of that row or column. The other position is left blank. In this next example, I index an entire column. Since row comes before column, I leave the row blank.

```
entire_matrix[ , "budget_millions"]
```

```
endgame avatar titanic star_wars
356 237 200 245
infinity_war jurassic_world
316 150
```

I could also index to select multiple rows and columns. If I want to extract the **year**, **runtime_minutes** and **budget_millions** columns, I would write:

```
entire_matrix[,c("year", "runtime_minutes", "budget_millions")]
```

```
year runtime_minutes budget_millions
endgame 2019 181 356
avatar 2009 162 237
titanic 1997 194 200
star_wars 2015 138 245
infinity_war 2018 149 316
jurassic_world 2015 124 150
```

```
entire_matrix[,c(2,3,4)]
```

```
year runtime_minutes budget_millions
endgame 2019 181 356
avatar 2009 162 237
titanic 1997 194 200
star_wars 2015 138 245
infinity_war 2018 149 316
jurassic_world 2015 124 150
```

If I want to extract the **star_wars**, **infinity_war** and **jurassic_world** rows, I would write:

```
entire_matrix[c("star_wars","infinity_war","jurassic_world"), ]
```

```
rank year runtime_minutes budget_millions
star_wars 4 2015 138 245
infinity_war 5 2018 149 316
jurassic_world 6 2015 124 150
domestic_opening_millions domestic_gross_millions
star_wars 248 937
infinity_war 258 679
jurassic_world 209 652
```

```
entire_matrix[c(4,5,6), ]
```

```
rank year runtime_minutes budget_millions
star_wars 4 2015 138 245
infinity_war 5 2018 149 316
jurassic_world 6 2015 124 150
domestic_opening_millions domestic_gross_millions
star_wars 248 937
infinity_war 258 679
jurassic_world 209 652
```

I can use the **rank()** function to specify the categories I want to rank the films by. This function returns a vector of numeric values.

```
rank(entire_matrix[,"domestic_opening_millions"])
```

```
endgame avatar titanic star_wars
6 2 1 4
infinity_war jurassic_world
5 3
```

This last section of this post is going to cover calculating the sum of values in a vector and a matrix.

I can calculate the sum of the values in a vector or matrix using the **sum()** function.

Let’s recall the original vector I created called **titanic**.

```
titanic <-c(3, 1997, 194, 200, 28)
```

I want to add these values in the vector. To do that, I would write this:

```
sum(titanic)
```

`[1] 2422`

As you can see the sum of this vector is 2422. What if I wanted to calculate all the values of the **titanic** row of my matrix?

```
sum(entire_matrix["titanic", ])
```

`[1] 3081`

Here the sum of value in my **titanic** row is 3081. Why are the two sums different? Remember that I added the **domestic_gross_millions** column to my matrix after the matrix was created. The original vector does not include the value for **domestic_gross_millions**.

Just as I did the sum of the values in a row, I can do the same for a column. If I want to add up all the values in **domestic_opening_millions** column, I would type the following:

```
sum(entire_matrix[, "domestic_opening_millions"])
```

`[1] 1177`

So the sum of all the values in the **domestic_opening_millions** column is 1177. This means that combined opening weekend total for all the films is about $1,117,000,000!

This just about does it for matrices in R! For the next post, I’ll get into lists in R.

For attribution, please cite this work as

Brantley (2020, Jan. 23). Data Sci Dani: Working With Matrices. Retrieved from https://datascidani.com/posts/working_with_matrices 01-23-20/

BibTeX citation

@misc{brantley2020working, author = {Brantley, Danielle}, title = {Data Sci Dani: Working With Matrices}, url = {https://datascidani.com/posts/working_with_matrices 01-23-20/}, year = {2020} }