Partial Order Defined By A Convex Cone
A pointed and salient convex cone C induces a partial ordering "≤" on V, defined so that x≤y if and only if y − x C. (If the cone is flat, the same definition gives merely a preorder.) Sums and positive scalar multiples of valid inequalities with respect to this order remain valid inequalities. A vector space with such an order is called an ordered vector space. Examples include the product order on real-valued vectors and the Loewner order on matrices.
Read more about this topic: Convex Cone
Famous quotes containing the words partial, order and/or defined:
“There is no luck in literary reputation. They who make up the final verdict upon every book are not the partial and noisy readers of the hour when it appears; but a court as of angels, a public not to be bribed, not to be entreated, and not to be overawed, decides upon every man’s title to fame. Only those books come down which deserve to last.”
—Ralph Waldo Emerson (1803–1882)
“It is not enough for theory to describe and analyse, it must itself be an event in the universe it describes. In order to do this theory must partake of and become the acceleration of this logic. It must tear itself from all referents and take pride only in the future. Theory must operate on time at the cost of a deliberate distortion of present reality.”
—Jean Baudrillard (b. 1929)
“The cliché that women, more consistently than men, turn inward for sustenance seems to mean, in practice, that women have richly defined the ways in which imagination creates possibility; possibility that society denies.”
—Patricia Meyer Spacks (b. 1929)