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:
“And DANTE searched the triple spheres,
Moulding nature at his will,
So shaped, so colored, swift or still,
And, sculptor-like, his large design
Etched on Alp and Apennine.”
—Ralph Waldo Emerson (1803–1882)
“These facts have always suggested to man the sublime creed that the world is not the product of manifold power, but of one will, of one mind; and that one mind is everywhere active, in each ray of the star, in each wavelet of the pool; and whatever opposes that will is everywhere balked and baffled, because things are made so, and not otherwise.”
—Ralph Waldo Emerson (1803–1882)
“A few days later the younger son gathered all he had and traveled to a distant country, and there he squandered his property in dissolute living.”
—Bible: New Testament, Luke 15:13.