Description: The following definitions for Form 195 are from Harazisville (see Kharazishvili [1979] )

Content:

The following definitions for Form 195 are from Harazisville (see Kharazishvili [1979] )

Definition:  

  1. If \(X\) and \(Y\) are vector spaces over a field \(K\) then a general linear system is a relation \(S\subseteq X\times Y\) which has domain \(X\) and is a subspace of\(X\times Y\).
  2. If \(S\) is as in 1. then a linear global reaction of \(S\) is a function \(\Phi : C \times X\rightarrow Y\) such that
    1. \(C\) is a vector space over \(K\)
    2. \(\Phi \) is a global reaction of \(S\) (i.e., \((x,y)\in S\) iff \(x\in X\) and \((\exists c)(c\in C\) and \(y = \Phi(c,x)).)\)
    3. There are linear functions \(\Phi_{1} : C\rightarrow  Y\) and \(\Phi_2 : X\rightarrow Y\) such that \(\Phi(c,x) = \Phi_{1}(c) + \Phi_{2}(x)\).

Howard-Rubin number: 62

Type: Definitions

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