proposition 5.75 Eigenvectors for distinct eigenvalues are independent
open in the book ·
parts/02-mathematical-methods/03-linear-algebra-representations.tex:3326
· p. 136
Rests on
-
depends_on
definition 5.69
Eigenvector, eigenvalue, eigenspace
¶
-
depends_on
definition 5.56
Endomorphism
¶
-
depends_on
definition 5.37
Linear transformation
¶
- depends_on definition 4.33 Vector space ¶
-
depends_on
definition 5.37
Linear transformation
¶
-
depends_on
definition 5.39
Kernel, image, nullity, rank
¶
- depends_on definition 5.37 Linear transformation ¶ ↺
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depends_on
definition 5.7
Vector subspace
¶
-
depends_on
definition 5.5
Linear combination
¶
- depends_on definition 4.33 Vector space ¶ ↺
-
depends_on
definition 5.5
Linear combination
¶
- proves proof ch:03-linear-algebra-representations@proof-12 ¶
-
depends_on
definition 5.56
Endomorphism
¶
-
depends_on
definition 5.14
Linear independence
¶
- depends_on definition 5.5 Linear combination ¶ ↺
- proves proof ch:03-linear-algebra-representations@proof-29 ¶
Supports
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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 ¶
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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 ¶
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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 ¶
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depends_on
proposition 32.39
Stability of a periodic orbit
¶
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 |
→ | Eigenvector, eigenvalue, eigenspace | declared | parts/02-mathematical-methods/03-linear-algebra-representations.tex:3331 |
depends_on |
→ | Linear independence | declared | parts/02-mathematical-methods/03-linear-algebra-representations.tex:3331 |
depends_on |
← | Criterion for diagonalizability | declared | parts/02-mathematical-methods/03-linear-algebra-representations.tex:3370 |
proves |
← | ch:03-linear-algebra-representations@proof-29 | declared | parts/02-mathematical-methods/03-linear-algebra-representations.tex:3334 |