proposition 5.107 The union of two subspaces

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:4645 · p. 150

Rests on

depends_on definition 5.5 Linear combination ¶
- depends_on definition 4.33 Vector space ¶
  - depends_on definition 4.8 Commutativity; abelian structure ¶
    - depends_on definition 4.4 Internal binary operation; magma ¶
      - depends_on definition 4.3 Algebraic structure ¶
      - depends_on definition 4.2 Binary operation ¶
  - depends_on definition 4.32 Field ¶
    - depends_on definition 4.11 Inverse element ¶
      - depends_on definition 4.9 Neutral element ¶
    - depends_on definition 4.20 Monoid ¶
      - depends_on definition 4.9 Neutral element ¶ ↺
      - depends_on definition 4.18 Semigroup ¶
    - depends_on definition 4.30 Ring ¶
      - depends_on definition 4.8 Commutativity; abelian structure ¶ ↺
      - depends_on definition 4.28 Distributivity ¶
      - depends_on definition 4.21 Group ¶
      - depends_on definition 4.18 Semigroup ¶ ↺
  - depends_on definition 4.31 Module ¶
    - depends_on definition 4.29 Action ¶
      - depends_on definition 4.9 Neutral element ¶ ↺
    - depends_on definition 4.28 Distributivity ¶ ↺
    - depends_on definition 4.21 Group ¶ ↺
    - depends_on definition 4.30 Ring ¶ ↺
depends_on definition 5.7 Vector subspace ¶
- depends_on definition 5.5 Linear combination ¶ ↺
proves proof ch:03-linear-algebra-representations@proof-49 ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Linear combination	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4650
`depends_on`	→	Vector subspace	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4650
`depends_on`	←	The sum is the right operation	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4681
`depends_on`	←	Two lines in physical space	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4712
`proves`	←	ch:03-linear-algebra-representations@proof-49	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4653