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|
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