definition 5.122 Linear hull

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:5265 · p. 158

ground object -- no derivation owed

Rests on

depends_on definition 5.121 Algebra ¶
- 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 4.1 Cartesian product ¶
      - depends_on definition 3.43 Map ¶
  - depends_on definition 4.2 Binary operation ¶ ↺
- 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 4.32 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 ¶ ↺

Supports

depends_on definition 5.124 Ideal ¶
- depends_on proposition 5.164 The kernel is an ideal ¶
  - depends_on corollary 5.168 cor:rep-adjoint-faithful ¶
depends_on definition 5.123 Subalgebra ¶

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`	→	Algebra	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:5271
`depends_on`	←	Ideal	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:5299
`depends_on`	←	Subalgebra	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:5287