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)
“Humour is the describing the ludicrous as it is in itself; wit is the exposing it, by comparing or contrasting it with something else. Humour is, as it were, the growth of nature and accident; wit is the product of art and fancy.”
—William Hazlitt (1778–1830)
“By rendering the labor of one, the property of the other, they cherish pride, luxury, and vanity on one side; on the other, vice and servility, or hatred and revolt.”
—James Madison (1751–1836)