definition 5.117 Signature

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:5051 · p. 155

ground object -- no derivation owed

Rests on

depends_on definition 5.113 Non-degenerate form ¶
- depends_on definition 5.110 Bilinear map ¶
  - depends_on definition 5.37 Linear transformation ¶
    - 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 theorem 5.116 Sylvester's law of inertia ¶
- depends_on definition 5.110 Bilinear map ¶ ↺
- depends_on definition 5.111 Symmetric and antisymmetric forms ¶
  - depends_on definition 5.110 Bilinear map ¶ ↺
  - depends_on equation 5.137 eq:lin-bilinear-matrix ¶
- depends_on equation 5.139 eq:lin-bilinear-congruence ¶
- proves proof ch:03-linear-algebra-representations@proof-53 ¶

Supports

depends_on proposition 5.94 Principal axes of a real quadratic form ¶
- depends_on proposition 5.95 The focal polar equation of a conic ¶

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`	→	Non-degenerate form	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:5056
`depends_on`	→	Sylvester's law of inertia	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:5056
`depends_on`	←	Principal axes of a real quadratic form	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4107