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 seashore is a sort of neutral ground, a most advantageous point from which to contemplate this world. It is even a trivial place. The waves forever rolling to the land are too far-traveled and untamable to be familiar. Creeping along the endless beach amid the sun-squall and the foam, it occurs to us that we, too, are the product of sea-slime.”
—Henry David Thoreau (1817–1862)
“As a man is said to have a right to his property, he may equally be said to have a property in his rights.”
—James Madison (1751–1836)