What does mean conv{e_1,−e_l,…,e_d,−e_d} and conv{{+1,-1}^d}. I could not understand, need a simple explanation.

Lyla Carson 2022-09-23 Answered
What does mean c o n v { e 1 , e l , , e d , e d } and c o n v { { + 1 , 1 } d } .
I could not understand, need a simple explanation.
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Answers (1)

Cremolinoer
Answered 2022-09-24 Author has 11 answers
Let us consider the case d=3.
The set { { + 1 , 1 } d } is the set of all triples (there are 2 3 = 8 of them)
{ ( 1 , 1 , 1 ) , ( 1 , 1 , 1 ) , ( 1 , 1 , 1 ) , ( 1 , 1 , 1 ) }
i.e., the vertices of a cube.
More generally, { + 1 , 1 } d is the set of vertices of a hypercube in R d
As a consequence:
c o n v { { + 1 , 1 } d }
is the "solid hypercube" in R d
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