definition 5.103 Sum of subspaces; internal direct sum

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:4463 · p. 148

Rests on

depends_on definition 5.101 External direct sum ¶
- 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 5.5 Linear combination ¶
  - depends_on definition 4.33 Vector space ¶ ↺
depends_on definition 5.7 Vector subspace ¶
- depends_on definition 5.5 Linear combination ¶ ↺

depends_on corollary 5.108 The sum is the right operation ¶
- depends_on example 5.109 Two lines in physical space ¶
depends_on proposition 5.104 Criterion for a direct sum ¶
depends_on proposition 5.105 Grassmann's formula ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	External direct sum	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4478
`depends_on`	→	Vector subspace	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4478
`depends_on`	←	The sum is the right operation	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4681
`depends_on`	←	Criterion for a direct sum	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4496
`depends_on`	←	Grassmann's formula	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4531