definition 5.73 Algebraic and geometric multiplicity

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:3268 · p. 135

ground object -- no derivation owed

Rests on

depends_on definition 5.70 Characteristic polynomial ¶
- depends_on definition 5.56 Endomorphism ¶
  - 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 equation 5.19 eq:lin-leibniz-det ¶
- depends_on equation 5.74 eq:lin-matrix-rep ¶
- proves proof ch:03-linear-algebra-representations@proof-25 ¶
depends_on definition 5.69 Eigenvector, eigenvalue, eigenspace ¶
- depends_on definition 5.56 Endomorphism ¶ ↺
- depends_on definition 5.39 Kernel, image, nullity, rank ¶
  - depends_on definition 5.37 Linear transformation ¶ ↺
  - depends_on definition 5.7 Vector subspace ¶
    - depends_on definition 5.5 Linear combination ¶
      - depends_on definition 4.33 Vector space ¶ ↺
  - proves proof ch:03-linear-algebra-representations@proof-12 ¶

Supports

depends_on proposition 5.74 prop:lin-geometric-le-algebraic ¶

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`	→	Characteristic polynomial	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:3274
`depends_on`	→	Eigenvector, eigenvalue, eigenspace	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:3274
`depends_on`	←	prop:lin-geometric-le-algebraic	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:3280