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Cone (linear algebra)
In linear algebra, a (linear) cone is a subset of a vector space that is closed under multiplication by positive scalars. In other words, a subset ''C'' of a real vector space ''V'' is a cone if and only if λ''x'' belongs to ''C'' for any ''x'' in ''C'' and any positive scalar λ of ''V'' (or, more succinctly, if and only if λ''C'' = ''C'' for any positive scalar λ).
A cone is said to be pointed if it includes the null vector (origin) 0; otherwise it is said to be blunt. Some authors use "non-negative" instead of "positive" in this definition of "cone", which restricts the term to the pointed cones only. In other contexts, a cone is pointed if the only linear subspace contained in it is .
The definition makes sense for any vector space ''V'' which allows the notion of "positive scalar" (i.e., where the ground field is an ordered field), such as spaces over the rational, real algebraic, or (most commonly) real numbers.
The concept can also be extended for any vector space ''V'' whose scalar field is a superset of those fields (such as the complex numbers, quaternions, etc.), to the extent that such a space can be viewed as a real vector space of higher dimension.
==Related concepts==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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