definition 5.76 Diagonalizable operator

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:3357 · p. 136

ground object -- no derivation owed

Rests on

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 4.4 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 equation 5.74 eq:lin-matrix-rep ¶

Supports

depends_on corollary 5.99 Semisimple and nilpotent parts ¶
depends_on theorem 5.77 Criterion for diagonalizability ¶
- depends_on proposition 32.39 Stability of a periodic orbit ¶
  - depends_on phenomenon 32.87 Universal period doubling ¶
  - depends_on proposition 32.84 Fixed points and the first period doubling ¶
    - depends_on phenomenon 32.87 Universal period doubling ¶ ↺
- depends_on theorem 32.13 Linear stability ¶
  - depends_on proposition 32.65 Fixed points of the Lorenz system and their stability ¶
  - depends_on proposition 32.23 Saddle-node bifurcation ¶
    - depends_on proposition 32.95 Intermittency: the scaling of the laminar phase ¶
  - depends_on proposition 32.24 Transcritical and pitchfork bifurcations ¶
  - depends_on proposition 28.69 Which branch is stable, and where it ends ¶

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`	→	Endomorphism	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:3361
`depends_on`	→	eq:lin-matrix-rep	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:3361
`depends_on`	←	Semisimple and nilpotent parts	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4372
`depends_on`	←	Criterion for diagonalizability	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:3370