example 5.109 Two lines in physical space

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:4697 · p. 151

example -- no derivation owed by its kind

Rests on

depends_on corollary 5.108 The sum is the right operation ¶
- depends_on definition 5.12 Subspace generated by a set of vectors ¶
  - 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 4.32 Field ¶
      - depends_on definition 4.31 Module ¶
  - depends_on definition 5.7 Vector subspace ¶
    - depends_on definition 5.5 Linear combination ¶ ↺
  - proves proof ch:03-linear-algebra-representations@proof-3 ¶
- depends_on definition 5.103 Sum of subspaces; internal direct sum ¶
  - depends_on definition 5.101 External direct sum ¶
    - depends_on definition 4.33 Vector space ¶ ↺
    - depends_on definition 5.5 Linear combination ¶ ↺
  - depends_on definition 5.7 Vector subspace ¶ ↺
- depends_on proposition 5.107 The union of two subspaces ¶
  - depends_on definition 5.5 Linear combination ¶ ↺
  - depends_on definition 5.7 Vector subspace ¶ ↺
  - proves proof ch:03-linear-algebra-representations@proof-49 ¶
- proves proof ch:03-linear-algebra-representations@proof-50 ¶
depends_on proposition 5.107 The union of two subspaces ¶ ↺

Supports

Nothing declares a dependency on this node yet.

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	The sum is the right operation	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4712
`depends_on`	→	The union of two subspaces	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4712