Treatise of Physics

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proposition 13.6 Levi-Civita identities in three dimensions

open in the book · parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:502 · p. 456

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proposition 13.6: Levi-Civita identities in three dimensions13.6definition 13.5: Tensor under orthogonal transformations13.5equation 5.19: eq:lin-leibniz-det5.19proposition 13.96: The cross product is an axial vector13.96proposition 13.95: The elementary cross-product identities13.95proof : ch:11-manifolds-tensors-curvature@proof-1proofdefinition 13.4: Orthogonal coordinate transformation13.4definition 19.42: Inertia tensor19.42definition 29.13: Inertia tensor, continuum form29.13lemma 30.26: Isotropic Cartesian tensors of rank four30.26notation 30.1: Strain and displacement share a letter30.1proposition 30.7: Strain is a Cartesian tensor of rank two30.7proposition 19.43: The moment of inertia is a quadratic form in the axis19.43remark 13.7: What the classification is used for13.7theorem 30.18: Cauchy: the stress tensor exists30.18definition A.508: Primitive mapA.508definition 5.58: Special linear group5.58definition 5.70: Characteristic polynomial5.70lemma A.497: The determinant is multiplicativeA.497lemma A.507: Coordinate permutationsA.507lemma 5.33: Determinant through the Levi–Civita symbol5.33lemma 5.137: The alternating top form is unique up to scale5.137proposition 7.111: Jacobi's formula, cofactor form7.111proposition 5.74: prop:lin-geometric-le-algebraic5.74proposition 5.2: Jacobi's formula, column form5.2equation 13.13: eq:mfd-condorto13.13proof : ch:11-manifolds-tensors-curvature@proof-19proofequation 13.225: eq:mfd-tprod313.225proof : ch:11-manifolds-tensors-curvature@proof-18proof

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depends_on → Tensor under orthogonal transformations declared parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:520
depends_on → eq:lin-leibniz-det declared parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:520
depends_on ← The cross product is an axial vector declared parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:4700
depends_on ← The elementary cross-product identities declared parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:4657
proves ← ch:11-manifolds-tensors-curvature@proof-1 declared parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:523