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)
““Courage!” he said, and pointed toward the land,
“This mounting wave will roll us shoreward soon.”
In the afternoon they came unto a land
In which it seemed always afternoon.”
—Alfred Tennyson (1809–1892)
“...there was the annual Fourth of July picketing at Independence Hall in Philadelphia. ...I thought it was ridiculous to have to go there in a skirt. But I did it anyway because it was something that might possibly have an effect. I remember walking around in my little white blouse and skirt and tourists standing there eating their ice cream cones and watching us like the zoo had opened.”
—Martha Shelley, U.S. author and social activist. As quoted in Making History, part 3, by Eric Marcus (1992)