proposition 5.74 prop:lin-geometric-le-algebraic

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:3277 · p. 135

Rests on

depends_on definition 5.73 Algebraic and geometric multiplicity ¶
- 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 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 ¶
    - proves proof ch:03-linear-algebra-representations@proof-12 ¶
depends_on equation 5.19 eq:lin-leibniz-det ¶ ↺
depends_on lemma 5.38 Exchange and completion ¶
- depends_on definition 5.15 Basis ¶
  - depends_on definition 5.12 Subspace generated by a set of vectors ¶
    - depends_on definition 5.5 Linear combination ¶ ↺
    - depends_on definition 5.7 Vector subspace ¶ ↺
    - proves proof ch:03-linear-algebra-representations@proof-3 ¶
  - depends_on definition 5.14 Linear independence ¶
    - depends_on definition 5.5 Linear combination ¶ ↺
- depends_on definition 5.12 Subspace generated by a set of vectors ¶ ↺
- depends_on definition 5.14 Linear independence ¶ ↺
- proves proof ch:03-linear-algebra-representations@proof-11 ¶
proves proof ch:03-linear-algebra-representations@proof-28 ¶

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type	direction	node	provenance	where
`depends_on`	→	Algebraic and geometric multiplicity	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:3280
`depends_on`	→	eq:lin-leibniz-det	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:3280
`depends_on`	→	Exchange and completion	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:3280
`proves`	←	ch:03-linear-algebra-representations@proof-28	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:3283