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:
“The triple pillar of the world transformed
Into a strumpet’s fool.”
—William Shakespeare (1564–1616)
“These facts have always suggested to man the sublime creed that the world is not the product of manifold power, but of one will, of one mind; and that one mind is everywhere active, in each ray of the star, in each wavelet of the pool; and whatever opposes that will is everywhere balked and baffled, because things are made so, and not otherwise.”
—Ralph Waldo Emerson (1803–1882)
“For wisdom is the property of the dead,
A something incompatible with life; and power,
Like everything that has the stain of blood,
A property of the living; but no stain
Can come upon the visage of the moon
When it has looked in glory from a cloud.”
—William Butler Yeats (1865–1939)