Attributes of matrices

The definition of a matrix necessitates the dim attribute for the object. This is present in every case, when a matrix is created, no matter what function was used to create it:

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

$dim
[1] 4 3

Similar vector’s names that can help with finding items in a vector, matrices also benefit from using names to identify values.

Names along the margins

The margins of a matrix refer to a dimension along which its values are organized. Two dimensional matrices have two margins: the rows and the columns (1 and 2). Accordingly, we can name the columns, using attributes similar to names: these atttributes are the column and the rrow names. THese are not set by default (as illustrated above), and in case they are queried with the colnames() and rownames() functions, they will be indicated to be absent by returning the value of NULL:

colnames(mat)

NULL

rownames(mat)

NULL

Setting row and column names

We can use replacement to set both the row and the column names, similar to names:

rownames(mat) <- letters[1:nrow(mat)]
colnames(mat) <- LETTERS[1:ncol(mat)]

Note that setting the colnames and rownames attribute will force the show() method to display the matrix with names along the margins, rather than the numeric subscript indices (e.g. [,1]).

You can query the set names the way, as with the names attribute:

rownames(mat)

[1] "a" "b" "c" "d"

colnames(mat)

[1] "A" "B" "C"

Partial setting of attributes

Note that both the regular names and the column and row names can be set partially, by replacing only specific elements. For instance if we want to keep the row names set above, but we would like to rename only the first column to something else, such as "x" we can do that, with replacing values in inside the attributes:

rownames(mat)[1] <- "x"
mat

Incorrect length of candidate attributes

Lets assume that we want to set the column names of this matrix:

m2 <- matrix(1:10, ncol=2, nrow=5)
m2

     [,1] [,2]
[1,]    1    6
[2,]    2    7
[3,]    3    8
[4,]    4    9
[5,]    5   10

Using a vector of incorrect length will result in an error, both when the vector is too short, or too long to become the name of the margin:

# Too short
rownames(m2) <- letters[1:4]

Error in dimnames(x) <- dn : 
  length of 'dimnames' [1] not equal to array extent

or:

# Too long 
rownames(m2) <- letters[1:6]

Error in dimnames(x) <- dn : 
  length of 'dimnames' [1] not equal to array extent

The truth about the row and column names: the `dimnames` attribute

This error might seem cryptic, as it refers to dimnames rather than row and column names. Technically speaking, both the row and column names are stored in the dimnames attribute, we just use the rownames() and colnames() functions to access these.

attributes(mat)

$dim
[1] 4 3

$dimnames
$dimnames[[1]]
[1] "x" "b" "c" "d"

$dimnames[[2]]
[1] "A" "B" "C"

Now this is getting complex looking - that is because the attributes and the dimnames inside them are stored using the list type, which can be recognized from the dollar $ symbols. This implementation allows more general use for n-dimensional matrices. We will learn how to interact directly with these later.

The lists are necessary because even though the same type is used for the row and column (or the nth dimension’s) names, their number can be different!