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:
“Their martyred blood and ashes sow
O’er all the Italian fields where still doth sway
The triple tyrant; that from these may grow
A hundredfold, who, having learnt thy way,
Early may fly the Babylonian woe.”
—John Milton (1608–1674)
“[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)
“I have no concern with any economic criticisms of the communist system; I cannot enquire into whether the abolition of private property is expedient or advantageous. But I am able to recognize that the psychological premises on which the system is based are an untenable illusion. In abolishing private property we deprive the human love of aggression of one of its instruments ... but we have in no way altered the differences in power and influence which are misused by aggressiveness.”
—Sigmund Freud (1856–1939)