Logical Entropy
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Table 4

Linearization of set concepts to corresponding vector-space concepts.

Set concept Vector-space concept
Universe set U Basis set of a space V
Cardinality of a set U Dimension of a space V
Subset of a set U Subspace of a space V
Partition of a set U Direct-sum decomposition of a space V
Numerical attribute Diagonalizable linear op. F: VV
Value r in image f(U) of f Eigenvalue λi of F
Constant set of Eigenvector v of F
Set of constant -sets ℘(f −1(r)) Eigenspace Vi of λi
Direct product of sets Tensor product of spaces
Elements of U × U Basis vectors of V ⊗ V