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)
“[The political mind] is a strange mixture of vanity and timidity, of an obsequious attitude at one time and a delusion of grandeur at another time. The political mind is the product of men in public life who have been twice spoiled. They have been spoiled with praise and they have been spoiled with abuse.”
—Calvin Coolidge (1872–1933)
“No man acquires property without acquiring with it a little arithmetic, also.”
—Ralph Waldo Emerson (1803–1882)