In mathematics, Choi's theorem on completely positive maps (after Man-Duen Choi) is a result that classifies completely positive maps between finite-dimensional (matrix) C*-algebras. An infinite-dimensional algebraic generalization of Choi's theorem is known as Belavkin's "Radon–Nikodym" theorem for completely positive maps.
Read more about Choi's Theorem On Completely Positive Maps: Some Preliminary Notions
Famous quotes containing the words theorem, completely, positive and/or maps:
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)
“Ideals possess the strange quality that if they were completely realized they would turn into nonsense. One could easily follow a commandment such as “Thou shalt not kill” to the point of dying of starvation; and I might establish the formula that for the proper functioning of the mesh of our ideals, as in the case of a strainer, the holes are just as important as the mesh.”
—Robert Musil (1880–1942)
“The oaks, how subtle and marine!
Bearded, and all the layered light
Above them swims; and thus the scene,
Recessed, awaits the positive night.”
—Robert Penn Warren (1905–1989)
“Living in cities is an art, and we need the vocabulary of art, of style, to describe the peculiar relationship between man and material that exists in the continual creative play of urban living. The city as we imagine it, then, soft city of illusion, myth, aspiration, and nightmare, is as real, maybe more real, than the hard city one can locate on maps in statistics, in monographs on urban sociology and demography and architecture.”
—Jonathan Raban (b. 1942)