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)
“Culture is a sham if it is only a sort of Gothic front put on an iron building—like Tower Bridge—or a classical front put on a steel frame—like the Daily Telegraph building in Fleet Street. Culture, if it is to be a real thing and a holy thing, must be the product of what we actually do for a living—not something added, like sugar on a pill.”
—Eric Gill (1882–1940)
“In the Greek cities, it was reckoned profane, that any person should pretend a property in a work of art, which belonged to all who could behold it.”
—Ralph Waldo Emerson (1803–1882)