Examples
Any scalar product on a real vector space V is a pairing (set M = N = V, R = R in the above definitions).
The determinant map (2 × 2 matrices over k) → k can be seen as a pairing .
The Hopf map written as is an example of a pairing. In for instance, Hardie et al. present an explicit construction of the map using poset models.
Read more about this topic: Pairing
Famous quotes containing the word examples:
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)