2.3 Matrices

Matrices are rectangular objects that we can think of as being made up of vectors.

We can make matrices by binding vectors that already exist.

cbind(a, e)

##      a   e      
## [1,] "1" "AAAAa"
## [2,] "2" "AAAAb"
## [3,] "3" "AAAAc"
## [4,] "4" "AAAAd"
## [5,] "5" "AAAAe"

Or we can make an empty one to fill.

matrix(0, nrow = 3, ncol = 4)

##      [,1] [,2] [,3] [,4]
## [1,]    0    0    0    0
## [2,]    0    0    0    0
## [3,]    0    0    0    0

Or we can make one from scratch.

mat <- matrix(seq(1, 12), ncol = 3, nrow = 4)

We can do all of the things we did with vectors to matrices, but now we have more than one column, and official “rows” that we can also use to these ends:

ncol(mat) # Number of columns
nrow(mat) # Number of rows
length(mat) # Total number of entries
mat[2, 3] # Value of row 2, column 3
str(mat)

See how number of rows and columns is defined in data structure? With rows and columns, we can assign column names and row names.

colnames(mat) <- c("first", "second", "third")
rownames(mat) <- c("This", "is", "a", "matrix")

# Take a look
mat

##        first second third
## This       1      5     9
## is         2      6    10
## a          3      7    11
## matrix     4      8    12

We can also do math on matrices just like vectors, because matrices are just vectors smooshed into two dimensions (it’s totally a word).

mat * 2

##        first second third
## This       2     10    18
## is         4     12    20
## a          6     14    22
## matrix     8     16    24

All the same operations we did on vectors above…one example.

More on matrices as we need them. We won’t use these a lot in this module, but R relies heavily on matrices to do linear algebra behind the scenes in the models that we will be working with.