# Matrices

| September 10th, 2013

## What's a matrix?

In R, a matrix is a collection of elements of the same data type (numeric, character, or logical) arranged into a fixed number of rows and columns. Since you are only working with rows and columns, a matrix is called two-dimensional.

You can construct a matrix in R with the `matrix()` function. Consider the following example:

``````matrix(1:9, byrow = TRUE, nrow = 3)
``````

In the `matrix()` function:

• The first argument is the collection of elements that R will arrange into the rows and columns of the matrix. Here, we use `1:9` which is a shortcut for `c(1, 2, 3, 4, 5, 6, 7, 8, 9)`.
• The argument `byrow` indicates that the matrix is filled by the rows. If we want the matrix to be filled by the columns, we just place `byrow = FALSE`.
• The third argument `nrow` indicates that the matrix should have three rows.

### Instructions

Construct a matrix with 3 rows containing the numbers 1 up to 9, filled row-wise.

`# no pec` `# Construct a matrix with 3 rows that contain the numbers 1 up to 9` ```# Construct a matrix with 3 rows that contain the numbers 1 up to 9 matrix(1:9, byrow = TRUE, nrow = 3)``` ``` test_function("matrix", c("data", "byrow", "nrow"), incorrect_msg = "Have you correctly created the matrix? Have a look at the assignment, the answer is already given!") test_output_contains("matrix(1:9, byrow=TRUE, nrow=3)", incorrect_msg = "There seems to be an issue with the matrix definition. Have a look at the assignment, the answer is already given!") success_msg("Great! Continue to the next exercise.") ```

## Analyzing matrices, you shall

It is now time to get your hands dirty. In the following exercises you will analyze the box office numbers of the Star Wars franchise. May the force be with you!

In the editor, three vectors are defined. Each one represents the box office numbers from the first three Star Wars movies. The first element of each vector indicates the US box office revenue, the second element refers to the Non-US box office (source: Wikipedia).

In this exercise, you'll combine all these figures into a single vector. Next, you'll build a matrix from this vector.

### Instructions

• Use `c(new_hope, empire_strikes, return_jedi)` to combine the three vectors into one vector. Call this vector `box_office`.
• Construct a matrix with 3 rows, where each row represents a movie. Use the `matrix()` function to this. The first argument is the vector `box_office`, containing all box office figures. Next, you'll have to specify `nrow = 3` and `byrow = TRUE`. Name the resulting matrix `star_wars_matrix`.
`# no pec` ```# Box office Star Wars (in millions!) new_hope <- c(460.998, 314.4) empire_strikes <- c(290.475, 247.900) return_jedi <- c(309.306, 165.8) # Create box_office box_office <- # Construct star_wars_matrix star_wars_matrix <- ``` ```# Box office Star Wars (in millions!) new_hope <- c(460.998, 314.4) empire_strikes <- c(290.475, 247.900) return_jedi <- c(309.306, 165.8) # Create box_office box_office <- c(new_hope, empire_strikes, return_jedi) # Construct star_wars_matrix star_wars_matrix <- matrix(box_office, nrow = 3, byrow = TRUE) ``` ``` msg <- "Do not change anything about the box office variables `new_hope`, `empire_strikes` and `return_jedi`!" test_object("new_hope", undefined_msg = msg, incorrect_msg = msg) test_object("empire_strikes", undefined_msg = msg, incorrect_msg = msg) test_object("return_jedi", undefined_msg = msg, incorrect_msg = msg) test_object("box_office", incorrect_msg = "Have you correctly combined the values of `new_hope`, `empire_strikes` and `return_jedi` into the vector `box_office`?") test_function("matrix", c("data", "nrow", "byrow"), incorrect_msg = "Make sure to correctly specify the arguments you pass to `matrix()`: `box_office`, `nrow = 3`, `by_row = TRUE`.") test_object("star_wars_matrix", incorrect_msg = "Did you assign the result of the `matrix()` call to `star_wars_matrix`?") success_msg("The force is actually with you! Continue to the next exercise.") ```
• `box_office <- c(new_hope, empire_strikes, return_jedi)` will combine all numbers in the different vectors into a single vector with 6 elements.
• `matrix(box_office, nrow = ..., by_row ...)` is a template for the solution to the second instruction.

## Naming a matrix

To help you remember what is stored in `star_wars_matrix`, you would like to add the names of the movies for the rows. Not only does this help you to read the data, but it is also useful to select certain elements from the matrix.

Similar to vectors, you can add names for the rows and the columns of a matrix

``````rownames(my_matrix) <- row_names_vector
colnames(my_matrix) <- col_names_vector
``````

We went ahead and prepared two vectors for you: `region`, and `titles`. You will need these vectors to name the columns and rows of `star_wars_matrix`, respectively.

### Instructions

• Use `colnames()` to name the columns of `star_wars_matrix` with the `region` vector.
• Use `rownames()` to name the rows of `star_wars_matrix` with the `titles` vector.
• Print out `star_wars_matrix` to see the result of your work.
`# no pec` ```# Box office Star Wars (in millions!) new_hope <- c(460.998, 314.4) empire_strikes <- c(290.475, 247.900) return_jedi <- c(309.306, 165.8) # Construct matrix star_wars_matrix <- matrix(c(new_hope, empire_strikes, return_jedi), nrow = 3, byrow = TRUE) # Vectors region and titles, used for naming region <- c("US", "non-US") titles <- c("A New Hope", "The Empire Strikes Back", "Return of the Jedi") # Name the columns with region # Name the rows with titles # Print out star_wars_matrix``` ```# Box office Star Wars (in millions!) new_hope <- c(460.998, 314.4) empire_strikes <- c(290.475, 247.900) return_jedi <- c(309.306, 165.8) # Construct matrix star_wars_matrix <- matrix(c(new_hope, empire_strikes, return_jedi), nrow = 3, byrow = TRUE) # Vectors region and titles, used for naming region <- c("US", "non-US") titles <- c("A New Hope", "The Empire Strikes Back", "Return of the Jedi") # Name the columns with region colnames(star_wars_matrix) <- region # Name the rows with titles rownames(star_wars_matrix) <- titles # Print out star_wars_matrix star_wars_matrix``` ``` msg <- "Do not change anything about the box office variables `new_hope`, `empire_strikes` and `return_jedi`!" test_object("new_hope", undefined_msg = msg, incorrect_msg = msg) test_object("empire_strikes", undefined_msg = msg, incorrect_msg = msg) test_object("return_jedi", undefined_msg = msg, incorrect_msg = msg) msg <- "Don't change the contents of `star_wars_matrix`; only the names of the rows and columns!" test_object("star_wars_matrix", incorrect_msg = msg) msg <- "Don't change anything about the `region` and `titles` vectors that have been defined for you." test_object("region", undefined_msg = msg, incorrect_msg = msg) test_object("titles", undefined_msg = msg, incorrect_msg = msg) test_object("star_wars_matrix", eq_condition = "equal", incorrect_msg = "Did you set the row and column names of `star_wars_matrix` correctly? Use `colnames(star_wars_matrix) <- region` for the column names; do a similar thing to name the rows.") test_output_contains("star_wars_matrix", incorrect_msg = "Don't forget to print out `star_wars_matrix` after you've named the rows and columns.") success_msg("Great! You're on the way of becoming an R jedi! Continue to the next exercise.") ```

You can use `colnames(star_wars_matrix) <- region` to name the columns of `star_wars_matrix`. Do a similar thing to name the rows.

## Calculating the worldwide box office

The single most important thing for a movie in order to become an instant legend in Tinseltown is its worldwide box office figures.

To calculate the total box office revenue for the three Star Wars movies, you have to take the sum of the US revenue column and the non-US revenue column.

In R, the function `rowSums()` conveniently calculates the totals for each row of a matrix. This function creates a new vector:

``````rowSums(my_matrix)
``````

### Instructions

Calculate the worldwide box office figures for the three movies and put these in the vector named `worldwide_vector`.

`# no pec` ```# Construct star_wars_matrix box_office <- c(460.998, 314.4, 290.475, 247.900, 309.306, 165.8) star_wars_matrix <- matrix(box_office, nrow = 3, byrow = TRUE, dimnames = list(c("A New Hope", "The Empire Strikes Back", "Return of the Jedi"), c("US", "non-US"))) # Calculate worldwide box office figures worldwide_vector <- ``` ```# Construct star_wars_matrix box_office <- c(460.998, 314.4, 290.475, 247.900, 309.306, 165.8) star_wars_matrix <- matrix(box_office, nrow = 3, byrow = TRUE, dimnames = list(c("A New Hope", "The Empire Strikes Back", "Return of the Jedi"), c("US", "non-US"))) # Calculate worldwide box office figures worldwide_vector <- rowSums(star_wars_matrix)``` ``` msg <- "Do not change anything about the preset variables `box_office_all` and `star_wars_marix`!" test_object("box_office", undefined_msg = msg, incorrect_msg = msg) test_object("star_wars_matrix", undefined_msg = msg, incorrect_msg = msg) test_object("worldwide_vector", incorrect_msg = "Call `rowSums()` on `star_wars_matrix` and store the result in `worldwide_vector`.") success_msg("Well done! Continue to the next exercise.") ```

`rowSums(star_wars_matrix)` will calculate the sum of every row, so the total box office for each movie.

## Adding a column for the Worldwide box office

In the previous exercise you calculated the vector that contained the worldwide box office receipt for each of the three Star Wars movies. However, this vector is not yet part of `star_wars_matrix`.

You can add a column or multiple columns to a matrix with the `cbind()` function, which merges matrices and/or vectors together by column. For example:

``````big_matrix <- cbind(matrix1, matrix2, vector1 ...)
``````

### Instructions

Add `worldwide_vector` as a new column to the `star_wars_matrix` and assign the result to `all_wars_matrix`. Use the `cbind()` function.

`# no pec` ```# Construct star_wars_matrix box_office <- c(460.998, 314.4, 290.475, 247.900, 309.306, 165.8) star_wars_matrix <- matrix(box_office, nrow = 3, byrow = TRUE, dimnames = list(c("A New Hope", "The Empire Strikes Back", "Return of the Jedi"), c("US", "non-US"))) # The worldwide box office figures worldwide_vector <- rowSums(star_wars_matrix) # Bind the new variable worldwide_vector as a column to star_wars_matrix all_wars_matrix <- ``` ```# Construct star_wars_matrix box_office <- c(460.998, 314.4, 290.475, 247.900, 309.306, 165.8) star_wars_matrix <- matrix(box_office, nrow = 3, byrow = TRUE, dimnames = list(c("A New Hope", "The Empire Strikes Back", "Return of the Jedi"), c("US", "non-US"))) # The worldwide box office figures worldwide_vector <- rowSums(star_wars_matrix) # Bind the new variable worldwide_vector as a column to star_wars_matrix all_wars_matrix <- cbind(star_wars_matrix, worldwide_vector)``` ``` msg <- "Do not change anything about the preset variables `box_office_all` and `star_wars_marix`!" test_object("box_office", undefined_msg = msg, incorrect_msg = msg) test_object("star_wars_matrix", undefined_msg = msg, incorrect_msg = msg) test_object("worldwide_vector", incorrect_msg = "Store the result of `rowSums(star_wars_matrix)` in `worldwide_vector`.") msg <- "Have you correctly used `cbind()` to add `worldwide_vector` to `star_wars_matrix`? You should pass `star_wars_matrix` and `world_wide_vector` to `cbind()`, in this order. The resulting matrix, `all_wars_matrix`, should consist of three rows and three columns." test_object("all_wars_matrix", incorrect_msg = msg) success_msg("Nice job! After adding column to a matrix, the logical next step is adding rows. Learn how in the next exercise."); ```

In this exercise, you should pass two variables to `cbind()`: `star_wars_matrix` and `worldwide_vector`, in this order. Assign the result to `all_wars_matrix`.

Just like every action has a reaction, every `cbind()` has an `rbind()`. (We admit, we are pretty bad with metaphors.)

Your R workspace, where all variables you defined 'live' (check out what a workspace is), has already been initialized and contains two matrices:

• `star_wars_matrix` that we have used all along, with data on the first trilogy,
• `star_wars_matrix2`, with similar data for the second trilogy.

Type the name of these matrices in the console and hit Enter if you want to have a closer look. If you want to check out the contents of the workspace, you can type `ls()` in the console.

### Instructions

Use `rbind()` to paste together `star_wars_matrix` and `star_wars_matrix2`, in this order. Assign the resulting matrix to `all_wars_matrix`.

```# Construct matrix box_office_all <- c(461, 314.4, 290.5, 247.9, 309.3, 165.8) movie_names <- c("A New Hope","The Empire Strikes Back","Return of the Jedi") col_titles <- c("US","non-US") star_wars_matrix <- matrix(box_office_all, nrow = 3, byrow = TRUE, dimnames = list(movie_names, col_titles)) # Construct matrix2 box_office_all2 <- c(474.5, 552.5, 310.7, 338.7, 380.3, 468.5) movie_names2 <- c("The Phantom Menace", "Attack of the Clones", "Revenge of the Sith") star_wars_matrix2 <- matrix(box_office_all2, nrow=3, byrow = TRUE, dimnames = list(movie_names2, col_titles)) # remove all except all_wars_matrix rm(box_office_all) rm(movie_names) rm(col_titles) rm(box_office_all2) rm(movie_names2)``` ```# star_wars_matrix and star_wars_matrix2 are available in your workspace star_wars_matrix star_wars_matrix2 # Combine both Star Wars trilogies in one matrix all_wars_matrix <- ``` ```# star_wars_matrix and star_wars_matrix2 are available in your workspace star_wars_matrix star_wars_matrix2 # Combine both Star Wars trilogies in one matrix all_wars_matrix <- rbind(star_wars_matrix, star_wars_matrix2)``` ``` msg = "Do not override the variables that have been defined for you in the workspace (`star_wars_matrix` and `star_wars_matrix2`)." test_object("star_wars_matrix", eq_condition = "equal", undefined_msg = msg, incorrect_msg = msg) test_object("star_wars_matrix2", eq_condition = "equal", undefined_msg = msg, incorrect_msg = msg) test_object("all_wars_matrix", incorrect_msg = "Did you use the `rbind()` correctly to create `all_wars_matrix()`? `rbind()` should take two arguments: `star_wars_matrix` and `star_wars_matrix2`, in this order.") success_msg("Wonderful! Continue with the next exercise and see how you can combine the results of the `rbind()` function with the `colSums()` function!") ```

Bind the two matrices together like this: ``` rbind(matrix1, matrix2) ``` Assign the result to `all_wars_matrix`.

## The total box office revenue for the entire saga

Just like every `cbind()` has a `rbind()`, every `colSums()` has a `rowSums()`. Your R workspace already contains the `all_wars_matrix` that you constructed in the previous exercise; type `all_wars_matrix` to have another look. Let's now calculate the total box office revenue for the entire saga.

### Instructions

• Calculate the total revenue for the US and the non-US region and assign `total_revenue_vector`. You can use the `colSums()` function.
• Print out `total_revenue_vector` to have a look at the results.
`load(url("http://s3.amazonaws.com/assets.datacamp.com/course/intro_to_r/all_wars_matrix.RData"))` ```# all_wars_matrix is available in your workspace all_wars_matrix # Total revenue for US and non-US total_revenue_vector <- # Print out total_revenue_vector``` ```# all_wars_matrix is available in your workspace all_wars_matrix # Total revenue for US and non-US total_revenue_vector <- colSums(all_wars_matrix) # Print out total_revenue_vector total_revenue_vector``` ``` msg = "Do not change the contents of `all_wars_matrix`; it was created for you in the workspace." test_object("all_wars_matrix", eq_condition = "equal", undefined_msg = msg, incorrect_msg = msg) test_function("colSums", "x", incorrect_msg = "Did you use the `colSums()` function on the all_wars_matrix?") test_object("total_revenue_vector", incorrect_msg = "Have you correctly assigned the result of `colSums(all_wars_matrix)` to `total_revenue_vector`?") test_output_contains("total_revenue_vector", incorrect_msg = "Don't forget to print out `total_revenue_vector`!") success_msg("Bellissimo! Head over to the next exercise to learn matrix subsetting.") ```

You should use the `colSums()` function with `star_wars_matrix` as the argument to find the total box office per region.

## Selection of matrix elements

Similar to vectors, you can use the square brackets `[ ]` to select one or multiple elements from a matrix. Whereas vectors have one dimension, matrices have two dimensions. You should therefore use a comma to separate that what to select from the rows from that what you want to select from the columns. For example:

• `my_matrix[1,2]` selects the element at the first row and second column.
• `my_matrix[1:3,2:4]` results in a matrix with the data on the rows 1, 2, 3 and columns 2, 3, 4.

If you want to select all elements of a row or a column, no number is needed before or after the comma, respectively:

• `my_matrix[,1]` selects all elements of the first column.
• `my_matrix[1,]` selects all elements of the first row.

Back to Star Wars with this newly acquired knowledge! As in the previous exercise, `all_wars_matrix` is already available in your workspace.

### Instructions

• Select the non-US revenue for all movies (the entire second column of `all_wars_matrix`), store the result as `non_us_all`.
• Use `mean()` on `non_us_all` to calculate the average non-US revenue for all movies. Simply print out the result.
• This time, select the non-US revenue for the first two movies in `all_wars_matrix`. Store the result as `non_us_some`.
• Use `mean()` again to print out the average of the values in `non_us_some`.
`load(url("http://s3.amazonaws.com/assets.datacamp.com/course/intro_to_r/all_wars_matrix.RData"))` ```# all_wars_matrix is available in your workspace all_wars_matrix # Select the non-US revenue for all movies non_us_all <- # Average non-US revenue # Select the non-US revenue for first two movies non_us_some <- # Average non-US revenue for first two movies ``` ```# all_wars_matrix is available in your workspace all_wars_matrix # Select the non-US revenue for all movies non_us_all <- all_wars_matrix[,2] # Average non-US revenue mean(non_us_all) # Select the non-US revenue for first two movies non_us_some <- all_wars_matrix[1:2,2] # Average non-US revenue for first two movies mean(non_us_some)``` ``` msg = "Do not change the contents of `all_wars_matrix`; this matrix has already been created for you in the workspace." test_object("all_wars_matrix", undefined_msg = msg, incorrect_msg = msg) test_object("non_us_all", incorrect_msg = "Did you assign to `non_us_all` the entire second column of `all_wars_matrix`? You can use `[, 2]` to do this!") test_output_contains("mean(non_us_all)", incorrect_msg = "Have you calculated the average of the values in `non_us_all` by calling `mean(non_us_all)`? Simply print out the result.") test_object("non_us_some", incorrect_msg = "Did you assign to `non_us_some` the non-US revenue for the first two movies? You can use `[1:2,2]` to do this!") test_output_contains("mean(non_us_some)", incorrect_msg = "Have you calculated the average of the values in `non_us_some` by calling `mean(non_us_some)`? Simply print out the result.") success_msg("Nice one! Continue to the next exercise.") ```

You can select the entire second column of a matrix `my_matrix` with `my_matrix[,2]`.

## A little arithmetic with matrices

Similar to what you have learned with vectors, the standard operators like `+`, `-`, `/`, `*`, etc. work in an element-wise way on matrices in R.

For example, `2 * my_matrix` multiplies each element of `my_matrix` by two.

As a newly-hired data analyst for Lucasfilm, it is your job is to find out how many visitors went to each movie for each geographical area. You already have the total revenue figures in `all_wars_matrix`. Assume that the price of a ticket was 5 dollars. Simply dividing the box office numbers by this ticket price gives you the number of visitors.

### Instructions

• Divide `all_wars_matrix` by 5, giving you the number of visitors in millions. Assign the resulting matrix to `visitors`.
• Print out `visitors` so you can have a look.
`load(url("http://s3.amazonaws.com/assets.datacamp.com/course/intro_to_r/all_wars_matrix.RData"))` ```# all_wars_matrix is available in your workspace all_wars_matrix # Estimate the visitors visitors <- # Print the estimate to the console ``` ```# all_wars_matrix is available in your workspace all_wars_matrix # Estimate the visitors visitors <- all_wars_matrix / 5 # Print the estimate to the console visitors``` ``` msg = "Do not change the contents of `all_wars_matrix`; this matrix has already been created for you in the workspace." test_object("all_wars_matrix", undefined_msg = msg, incorrect_msg = msg) test_object("visitors", incorrect_msg = "It looks like `visitors` is not correct. Simply divide `all_wars_matrix` by 5 and store the resulting matrix as `visitors`.") test_output_contains("visitors", incorrect_msg = "Don't forget to also print out `visitors` so you can have a look.") success_msg("Great! What do these results tell you? A staggering 92 million people went to see A New Hope in US theaters! Continue to the next exercise.") ```

The number of visitors is equal to `all_wars_matrix` divided by 5.

## A little arithmetic with matrices (2)

Just like `2 * my_matrix` multiplied every element of `my_matrix` by two, `my_matrix1 * my_matrix2` creates a matrix where each element is the product of the corresponding elements in `my_matrix1` and `my_matrix2`.

After looking at the result of the previous exercise, big boss Lucas points out that the ticket prices went up over time. He asks to redo the analysis based on the prices you can find in `ticket_prices_matrix` (source: imagination).

Those who are familiar with matrices should note that this is not the standard matrix multiplication for which you should use `%*%` in R.

### Instructions

• Divide `all_wars_matrix` by `ticket_prices_matrix` to get the estimated number of US and non-US visitors for the six movies. Assign the result to `visitors`.
• From the `visitors` matrix, select the entire first column, representing the number of visitors in the US. Store this selection as `us_visitors`.
• Calculate the average number of US visitors; print out the result.
```load(url("http://s3.amazonaws.com/assets.datacamp.com/course/intro_to_r/all_wars_matrix.RData")) movie_names <- c("A New Hope","The Empire Strikes Back","Return of the Jedi", "The Phantom Menace", "Attack of the Clones", "Revenge of the Sith") col_titles <- c("US","non-US") ticket_prices_matrix <- matrix(c(5, 5, 6, 6, 7, 7, 4, 4, 4.5, 4.5, 4.9, 4.9), nrow = 6, byrow = TRUE, dimnames = list(movie_names,col_titles))``` ```# all_wars_matrix and ticket_prices_matrix are available in your workspace all_wars_matrix ticket_prices_matrix # Estimated number of visitors visitors <- # US visitors us_visitors <- # Average number of US visitors ``` ```# all_wars_matrix and ticket_prices_matrix are available in your workspace all_wars_matrix ticket_prices_matrix # Estimated number of visitors visitors <- all_wars_matrix / ticket_prices_matrix # US visitors us_visitors <- visitors[ ,1] # Average number of US visitors mean(us_visitors)``` ``` msg <- "Do not change the contents of `all_wars_matrix`; this matrix has already been created for you in the workspace." test_object("all_wars_matrix", undefined_msg = msg, incorrect_msg = msg) test_object("ticket_prices_matrix", undefined_msg = msg, incorrect_msg = msg) test_object("visitors", incorrect_msg = "Have you correctly created the `visitors` matrix? You should divide `all_wars_matrix` by `ticket_prices_matrix` to get there.") test_object("us_visitors", incorrect_msg = "To created `us_visitors`, you should correctly select the entire first column from `visitors`. You can use `[,1]` for this!") test_output_contains("mean(us_visitors)", incorrect_msg = "Once you have created `us_visitors`, you can use `mean()` to calculate the average number of visitors in the US. Make sure to print out the result.") success_msg("It's a fact: the R force is with you! This exercise concludes the chapter on matrices. Next stop on your journey through the R language: factors.") ```
• You can use the function `mean()` to calculate the average of the inputs to the function.
• To get the number of visitors in the US, select the first column from `visitors` using `visitors[ ,1]`.