External Binary Operations
An external binary operation is a binary function from K × S to S. This differs from a binary operation in the strict sense in that K need not be S; its elements come from outside.
An example of an external binary operation is scalar multiplication in linear algebra. Here K is a field and S is a vector space over that field.
An external binary operation may alternatively be viewed as an action; K is acting on S.
Note that the dot product of two vectors is not a binary operation, external or otherwise, as it maps from S× S to K, where K is a field and S is a vector space over K.
Read more about this topic: Binary Operation
Famous quotes containing the words external and/or operations:
“Without free, self-respecting, and autonomous citizens there can be no free and independent nations. Without internal peace, that is, peace among citizens and between the citizens and the state, there can be no guarantee of external peace.”
—Václav Havel (b. 1936)
“A sociosphere of contact, control, persuasion and dissuasion, of exhibitions of inhibitions in massive or homeopathic doses...: this is obscenity. All structures turned inside out and exhibited, all operations rendered visible. In America this goes all the way from the bewildering network of aerial telephone and electric wires ... to the concrete multiplication of all the bodily functions in the home, the litany of ingredients on the tiniest can of food, the exhibition of income or IQ.”
—Jean Baudrillard (b. 1929)