proposition 5.42 The adjoint exists, is unique, and is linear

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:1878 · p. 118

Rests on

depends_on definition 5.41 Adjoint ¶
- depends_on definition 5.18 Inner product ¶
  - 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 4.20 Monoid ¶
      - depends_on definition 4.30 Ring ¶
    - depends_on definition 4.31 Module ¶
      - depends_on definition 4.29 Action ¶
      - depends_on definition 4.28 Distributivity ¶
      - depends_on definition 4.21 Group ¶
      - depends_on definition 4.30 Ring ¶ ↺
- depends_on definition 5.37 Linear transformation ¶
  - depends_on definition 4.33 Vector space ¶ ↺
depends_on equation 5.74 eq:lin-matrix-rep ¶
depends_on proposition 5.28 Gram–Schmidt ¶
- depends_on definition 5.14 Linear independence ¶
  - depends_on definition 5.5 Linear combination ¶
    - depends_on definition 4.33 Vector space ¶ ↺
- depends_on definition 5.18 Inner product ¶ ↺
- depends_on definition 5.27 Orthonormal basis ¶
  - depends_on definition 5.26 Orthogonal basis ¶
    - depends_on definition 5.15 Basis ¶
      - depends_on definition 5.12 Subspace generated by a set of vectors ¶
      - depends_on definition 5.14 Linear independence ¶ ↺
    - depends_on definition 5.24 Orthogonal vectors ¶
      - depends_on definition 5.18 Inner product ¶ ↺
  - depends_on definition 5.25 Unit vector ¶
    - depends_on definition 5.19 Norm ¶
      - depends_on definition 4.33 Vector space ¶ ↺
- depends_on equation 5.44 eq:lin-norm-assoc ¶
- proves proof ch:03-linear-algebra-representations@proof-5 ¶
proves proof ch:03-linear-algebra-representations@proof-14 ¶

Supports

depends_on corollary 5.82 Spectral theorem for a normal operator ¶

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`	→	Adjoint	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:1890
`depends_on`	→	eq:lin-matrix-rep	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:1890
`depends_on`	→	Gram–Schmidt	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:1890
`depends_on`	←	Spectral theorem for a normal operator	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:3594
`proves`	←	ch:03-linear-algebra-representations@proof-14	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:1893