Everything about Convex Cone totally explained
In
linear algebra, a
convex cone is a
subset of a
vector space that's
closed under
linear combinations with positive coefficients.
Definition
A subset
C of a vector space
V is a
convex cone if and only if α
x + β
y belongs to
C, for any positive scalars α, β of
V, and any
x,
y in
C.
The defining condition can be written more succinctly as "α
C + β
C =
C for any positive scalars α, β of
V.
The concept is meaningful for any vector space that allows the concept of "positive" scalar, such as spaces over the
rational,
algebraic, or (more commonly) the
real numbers.
The empty set, the space
V, and any linear subspace of
V (including the trivial subspace .
Both the normal and tangent cone have the property of being closed and convex. They are important concepts in the fields of
convex optimization,
variational inequalities and
projected dynamical systems.
Further Information
Get more info on 'Convex Cone'.
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