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:

    “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)

    “Everything that is beautiful and noble is the product of reason and calculation.”
    —Charles Baudelaire (1821–1867)

    “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)