Conical combination

Given a finite number of vectors 
 
 
 
 
 x
 
 1
 
 
 ,
 
 x
 
 2
 
 
 ,
 …
 ,
 
 x
 
 n
 
 
 
 
 {\displaystyle x_{1},x_{2},\dots ,x_{n}}
 
 in a <a href="/facts/Real_number/R02gw5Pb">real</a> <a href="/facts/Vector_space/M1pxMLx2">vector space</a>, a conical combination, conical sum, or weighted sum of these vectors is a vector of the form

α
          
            1
          
        
        
          x
          
            1
          
        
        +
        
          α
          
            2
          
        
        
          x
          
            2
          
        
        +
        ⋯
        +
        
          α
          
            n
          
        
        
          x
          
            n
          
        
      
    
    {\displaystyle \alpha _{1}x_{1}+\alpha _{2}x_{2}+\cdots +\alpha _{n}x_{n}}

where 
 
 
 
 
 α
 
 i
 
 
 
 
 {\displaystyle \alpha _{i}}
 
 are <a href="/facts/Non-negative/z0xollg1">non-negative</a> real numbers.
The name derives from the fact that the set of all conical sum of vectors defines a <a href="/facts/Convex_cone/h1tARfw4">cone</a> (possibly in a lower-dimensional <a href="/facts/Linear_subspace/2wtKTgHL">subspace</a>).

Conical combination open-in-new

Conical combination