Triple Product Property

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

s's^{-1}t't^{-1}u'u^{-1} = 1 \Rightarrow s' = s, t' = t, u' = u

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 we fairies, that do run
    By the triple Hecate’s team
    From the presence of the sun,
    Following darkness like a dream,
    Now are frolic. Not a mouse
    Shall disturb this hallowed house.”
    —William Shakespeare (1564–1616)

    “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)

    “The second property of your excellent sherris is the warming
    of the blood.”
    —William Shakespeare (1564–1616)