A link matrix is a sequence of points (or lines) that represent linkages between words or phrases. The simplest matrix is an ordered list — a set of lists that are sorted according to their length, such as the one below. A list is ordered by its element length.

We can represent a word or phrase as a set of links and, hence, as a matrix. A word is a list of words. A phrase is a list of phrases.

Here’s a link matrix that tells you a couple of things: (1) words (lists) are linked in a way that a sentence alone does not; (2) a phrase is a list of links to other phrases; and (3) words and phrases are linked by their lengths.

The first element of a link matrix can be any element of the list of links (e.g., every element in a list is a link to the second element). This is true for the second element, too. This gives us a link matrix with entries for every element in every element in the entire (empty?) list of links.

Let’s say we have a list of “three phrases.” We want to represent this as a link matrix with the first four elements of each phrase representing links to the remaining two elements. These remaining two element are themselves links.

(1A) (2B) (3A) (2B) (3B) (4A) (4B)

This is a single word link matrix, and it is identical to the single sentence link matrix above.

The link matrix here could be represented using another element list (e.g., every link in the first element of A has a first element in B; or every link in B has a second element in A; or…). It works equally well with two-element lists and with one-element lists (e.g., the second element of A is the second element of B). This is just a way to organize other things into link matrixes — the link matrix itself doesn’t provide any properties that you need, but if you know what you’re doing it will work just fine.

Now let’s say we have a list of four phrases. We want to represent this as a link matrix with the second element representing links to the first element. The first two elements of this phrase are links to the remaining two elements. Here, it is very similar to the single phrase link matrix above. It works equally well

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