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:
- 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\(X\times Y\).
- If \(S\) is as in 1. then a linear global reaction of \(S\) is a function \(\Phi : C \times X\rightarrow Y\) such that
- \(C\) is a vector space over \(K\)
- \(\Phi \) is a global reaction of \(S\) (i.e., \((x,y)\in S\) iff \(x\in X\) and \((\exists c)(c\in C\) and \(y = \Phi(c,x)).)\)
- 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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