Blunt and Pointed Cones
According to the above definition, if C is a convex cone, then C{0} is a convex cone, too. A convex cone is said to be pointed or blunt depending on whether it includes the null vector 0 or not. Blunt cones can be excluded from the definition of convex cone by substituting "non-negative" for "positive" in the condition of α, β. The term "pointed" is also often used to refer to a closed cone that contains no complete line (i.e., no nontrivial subspace of the ambient vector space V), i.e. what is called a "salient" cone below.
Read more about this topic: Convex Cone
Famous quotes containing the words blunt, pointed and/or cones:
“Devouring Time, blunt thou the lion’s paws,
And make the earth devour her own sweet brood;
Pluck the keen teeth from the fierce tiger’s jaws,
And burn the long-liv’d phoenix in her blood;
Make glad and sorry seasons as thou fleet’st,
And do what’er thou wilt, swift-footed Time,
To the wide world and all her fading sweets;”
—William Shakespeare (1564–1616)
“Be sure that it is not you that is mortal, but only your body. For that man whom your outward form reveals is not yourself; the spirit is the true self, not that physical figure which can be pointed out by your finger.”
—Marcus Tullius Cicero (106–43 B.C.)
“Here was a little of everything in a small compass to satisfy the wants and the ambition of the woods,... but there seemed to me, as usual, a preponderance of children’s toys,—dogs to bark, and cats to mew, and trumpets to blow, where natives there hardly are yet. As if a child born into the Maine woods, among the pine cones and cedar berries, could not do without such a sugar-man or skipping-jack as the young Rothschild has.”
—Henry David Thoreau (1817–1862)