## 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 λ_{i} of F |

Constant set of | Eigenvector v of F |

Set of constant -sets ℘(f
^{−1}(r)) |
Eigenspace V_{i} of λ_{i} |

Direct product of sets | Tensor product of spaces |

Elements of U × U |
Basis vectors of V ⊗ V |