In abstract algebra, the triple product property is an identity satisfied in some groups.
Let be a non-trivial group. Three nonempty subsets are said to have the triple product property in if for all elements, it is the case that
where is the identity of .
It plays a role in research of fast matrix multiplication algorithms.
Famous quotes containing the words triple, product and/or property:
“The triple pillar of the world transformed
Into a strumpet’s fool.”
—William Shakespeare (1564–1616)
“Perhaps I am still very much of an American. That is to say, naïve, optimistic, gullible.... In the eyes of a European, what am I but an American to the core, an American who exposes his Americanism like a sore. Like it or not, I am a product of this land of plenty, a believer in superabundance, a believer in miracles.”
—Henry Miller (1891–1980)
“The charming landscape which I saw this morning is indubitably made up of some twenty or thirty farms. Miller owns this field, Locke that, and Manning the woodland beyond. But none of them owns the landscape. There is property in the horizon which no man has but he whose eye can integrate all parts, that is, the poet. This is the best part of these men’s farms, yet to this their warranty-deeds give no title.”
—Ralph Waldo Emerson (1803–1882)