simplexˈsɪm plɛks
simplex
English Definitions:
simplex (adj)
allowing communication in only one direction at a time, or in telegraphy allowing only one message over a line at a time
"simplex system"
simplex (adj)
having only one part or element
"a simplex word has no affixes and is not part of a compound--like `boy' compared with `boyish' or `house' compared with `houseboat'"
simplex (Noun)
An analogue in any dimension of the triangle or tetrahedron: the convex hull of n+1 points in n-dimensional space.
simplex (Noun)
A simple word, one without affixes.
simplex (Adjective)
Single, simple; not complex.
simplex (Adjective)
unidirectional
Simplex
In geometry, a simplex is a generalization of the notion of a triangle or tetrahedron to arbitrary dimension. Specifically, a k-simplex is a k-dimensional polytope which is the convex hull of its k + 1 vertices. More formally, suppose the k + 1 points are affinely independent, which means are linearly independent. Then, the simplex determined by them is the set of points . For example, a 2-simplex is a triangle, a 3-simplex is a tetrahedron, and a 4-simplex is a 5-cell. A single point may be considered a 0-simplex, and a line segment may be considered a 1-simplex. A simplex may be defined as the smallest convex set containing the given vertices. A regular simplex is a simplex that is also a regular polytope. A regular n-simplex may be constructed from a regular-simplex by connecting a new vertex to all original vertices by the common edge length. In topology and combinatorics, it is common to “glue together” simplices to form a simplicial complex. The associated combinatorial structure is called an abstract simplicial complex, in which context the word “simplex” simply means any finite set of vertices.
Simplex
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. For example, a 0-dimensional simplex is a point, a 1-dimensional simplex is a line segment, a 2-dimensional simplex is a triangle, a 3-dimensional simplex is a tetrahedron, and a 4-dimensional simplex is a 5-cell.Specifically, a k-simplex is a k-dimensional polytope which is the convex hull of its k + 1 vertices. More formally, suppose the k + 1 points u 0 , … , u k {\displaystyle u_{0},\dots ,u_{k}} are affinely independent, which means that the k vectors u 1 − u 0 , … , u k − u 0 {\displaystyle u_{1}-u_{0},\dots ,u_{k}-u_{0}} are linearly independent. Then, the simplex determined by them is the set of points A regular simplex is a simplex that is also a regular polytope. A regular k-simplex may be constructed from a regular (k − 1)-simplex by connecting a new vertex to all original vertices by the common edge length. The standard simplex or probability simplex is the k − 1 dimensional simplex whose vertices are the k standard unit vectors in R k {\displaystyle \mathbb {R} ^{k}} , or in other words In topology and combinatorics, it is common to "glue together" simplices to form a simplicial complex. The associated combinatorial structure is called an abstract simplicial complex, in which context the word "simplex" simply means any finite set of vertices.
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