Treatise of Physics

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theorem 5.77 Criterion for diagonalizability

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:3364 · p. 136

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theorem 5.77: Criterion for diagonalizability5.77definition 5.76: Diagonalizable operator5.76definition 5.69: Eigenvector, eigenvalue, eigenspace5.69proposition 5.75: Eigenvectors for distinct eigenvalues are independent5.75proposition 32.39: Stability of a periodic orbit32.39theorem 32.13: Linear stability32.13proof : ch:03-linear-algebra-representations@proof-30proofdefinition 5.56: Endomorphism5.56equation 5.74: eq:lin-matrix-rep5.74corollary 5.99: Semisimple and nilpotent parts5.99definition 5.39: Kernel, image, nullity, rank5.39corollary 9.25: Normal modes of a diagonalizable system9.25definition 5.73: Algebraic and geometric multiplicity5.73definition 9.30: Hyperbolic equilibrium9.30theorem 5.71: The eigenvalues are the roots of the characteristic polynomial5.71definition 5.14: Linear independence5.14proof : ch:03-linear-algebra-representations@proof-29proofdefinition 32.38: Poincaré section and return map32.38phenomenon 32.87: Universal period doubling32.87proposition 32.84: Fixed points and the first period doubling32.84proof : ch:15-nonlinear-dynamics-chaos@proof-14proofdefinition 32.12: Linearization32.12proposition 32.65: Fixed points of the Lorenz system and their stability32.65proposition 32.23: Saddle-node bifurcation32.23proposition 32.24: Transcritical and pitchfork bifurcations32.24proposition 28.69: Which branch is stable, and where it ends28.69proof : ch:15-nonlinear-dynamics-chaos@proof-4proof

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typedirectionnode provenancewhere
depends_on → Diagonalizable operator declared parts/02-mathematical-methods/03-linear-algebra-representations.tex:3370
depends_on → Eigenvector, eigenvalue, eigenspace declared parts/02-mathematical-methods/03-linear-algebra-representations.tex:3370
depends_on → Eigenvectors for distinct eigenvalues are independent declared parts/02-mathematical-methods/03-linear-algebra-representations.tex:3370
depends_on ← Stability of a periodic orbit declared parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:1015
depends_on ← Linear stability declared parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:291
proves ← ch:03-linear-algebra-representations@proof-30 declared parts/02-mathematical-methods/03-linear-algebra-representations.tex:3374