2.1 About Matrices

First let’s talk about matrices in the mathematical sense of the word. A matrix is a rectangular array of elements. More formally, a matrix is a mathematical object whose structure is a rectangular array of entries.

Typically, we consider the elements of a matrix to be numbers. Although you can certainly generalize the contents of a matrix and think about them as any type of symbols, not necessarily numbers. This is perhaps a common way to conceive a generic matrix from a more computational-oriented perspective.

From example, an R matrix may be numeric, but you can also have matrices containing logical values (TRUE or FALSE), or even a matrix made up of characters.

# numeric matrix
A <- matrix(1:12, nrow = 4, ncol = 3)
A
     [,1] [,2] [,3]
[1,]    1    5    9
[2,]    2    6   10
[3,]    3    7   11
[4,]    4    8   12
# logical matrix
L <- matrix(c(TRUE, FALSE), nrow = 4, ncol = 3)
L
      [,1]  [,2]  [,3]
[1,]  TRUE  TRUE  TRUE
[2,] FALSE FALSE FALSE
[3,]  TRUE  TRUE  TRUE
[4,] FALSE FALSE FALSE
# character matrix
S <- matrix(sample(letters, 12), nrow = 4, ncol = 3)
S
     [,1] [,2] [,3]
[1,] "c"  "e"  "o" 
[2,] "v"  "k"  "q" 
[3,] "w"  "z"  "u" 
[4,] "b"  "h"  "i"