VectorGreaterEqual 
xy or VectorGreaterEqual[{x,y}]
yields True for vectors of length n if xi≥yi for all components .
xκy or VectorGreaterEqual[{x,y},κ]
yields True for x and y if x-y∈κ, where κ is a proper convex cone.
Details


- VectorGreaterEqual gives a partial ordering of elements in a vector space that is still compatible with vector space operations.
- VectorGreaterEqual is typically used to specify vector inequalities for constrained optimization, inequality solving and integration.
- By using the character , entered as
v>=
or \[VectorGreaterEqual], with subscripts vector inequalities can be entered as follows:
-
VectorGreaterEqual[{x,y}] the standard vector inequality VectorGreaterEqual[{x,y},κ] vector inequality defined by a cone κ - xy remains unevaluated if x or y has a non-numeric element; typically gives True or False otherwise.
- When x and y are n-vectors, xy yields False if xi>yi for any component
.
- When x is an n-vector and y is a scalar, xy yields True if xi≥y for all components
.
- Possible cone specifications κ in
for vectors x include:
-
{"NonNegativeCone", n} such that
{"NormCone", n} such that Norm[{x1,…,xn-1}]≤xn
"ExponentialCone" such that
"DualExponentialCone" such that
or
{"PowerCone",α} such that
{"DualPowerCone",α} such that
- Possible cone specifications κ in
for matrices x include:
-
"NonNegativeCone" such that
{"SemidefiniteCone", n} symmetric positive semidefinite matrices - Possible cone specifications κ in
for arrays x include:
-
"NonNegativeCone" such that
- For exact numeric quantities, VectorGreaterEqual internally uses numerical approximations to establish numerical ordering. This process can be affected by the setting of the global variable $MaxExtraPrecision.
Examples
open allclose allBasic Examples (2)
Scope (7)
Determine if all of the elements in a vector are non-negative:
Determine if all components are less than or equal to 1:
For each component, !xi≥yi does imply xi<yi:
Compare the components of two matrices:
Represent the condition that Norm[{x,y}]<=1:
Applications (1)
VectorGreaterEqual is a fast way to compare many elements:
Text
Wolfram Research (2019), VectorGreaterEqual, Wolfram Language function, https://reference.wolfram.com/language/ref/VectorGreaterEqual.html.
BibTeX
BibLaTeX
CMS
Wolfram Language. 2019. "VectorGreaterEqual." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/VectorGreaterEqual.html.
APA
Wolfram Language. (2019). VectorGreaterEqual. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VectorGreaterEqual.html