I realize that not everyone understands how matrices work, but this is ridiculous. The abstract of the patent:
"... the rank of a document is calculated from a constant representing the probability that a browser through the database will randomly jump to the document."
And the specific claim is:
"Looked at another way, the importance of a page is directly related to the steady-state probability that a random web surfer ends up at the page after following a large number of links."
This _explicitly_ describes a Markov Chain, which is naturally represented by a matrix. A variety of versions of the linear equation are explicitly given in the patent.
To claim you can implement the patent without matrices is, for all intents and purposes, wrong. You can implement the same equations in a variety of ways, but they are still matrix equations.
They patented the idea to apply random walks to ranking webpages. That's arguably reasonably novel, though Wikipedia lists a number of predecessors. But it was also an inevitable invention, because there is a large number of people familiar with Random Walks/Markov Processes, they are routinely taught to undergrads, and are used to model and analyse a vast number of processes [1].
What you quoted is not what the patent “claims”. The claims are the numbered points in the section “Claims”. They are the only legally enforced section of a patent and they are written in a very specific language. Everything else is background or embodiment and has little to no legal value.
"... the rank of a document is calculated from a constant representing the probability that a browser through the database will randomly jump to the document."
And the specific claim is:
"Looked at another way, the importance of a page is directly related to the steady-state probability that a random web surfer ends up at the page after following a large number of links."
This _explicitly_ describes a Markov Chain, which is naturally represented by a matrix. A variety of versions of the linear equation are explicitly given in the patent.
To claim you can implement the patent without matrices is, for all intents and purposes, wrong. You can implement the same equations in a variety of ways, but they are still matrix equations.
They patented the idea to apply random walks to ranking webpages. That's arguably reasonably novel, though Wikipedia lists a number of predecessors. But it was also an inevitable invention, because there is a large number of people familiar with Random Walks/Markov Processes, they are routinely taught to undergrads, and are used to model and analyse a vast number of processes [1].
[1] https://en.wikipedia.org/wiki/Markov_chain#Applications