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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: V → V |
| 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 |