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15
296
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What is the coordinate-free definition of the Levi-Civita Symbol?

Published on
#differential-geometry #tensors
72
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Tensor cross product proof: $Sa \times Sb = \det(S)S^{-T}(a \times b)$

Published on
#tensor-products #tensors #cross-product #tensor-rank
353
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Why is the volume element unique in the way Spivak develops it?

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#linear-algebra #multivariable-calculus #tensors #volume #exterior-algebra
357
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Tensor contraction computation

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#tensor-products #tensors #contraction-operator
81
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Question on Partial derivatives in inverse function changing from coordinate systems

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#coordinate-systems #tensors #rotations #chain-rule #jacobian
118
Views

Simplification using suffix notation

Published on
#tensors
361
Views

Prove Poincaré Lemma for $1$-form

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#multivariable-calculus #closed-form #tensors #exterior-algebra #stokes-theorem
233
Views

Simplification of multiple Levi-Civita Epsilons

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#tensors
565
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Prove that the covariant derivative commutes with musical isomorphisms

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#differential-geometry #tensors #vector-fields #connections
101
Views

What is a neat way to solve $\nabla\mathbf{u}+\nabla\mathbf{u}^T=\mathbf{\mathbf{C}}$?

Published on
#multivariable-calculus #partial-differential-equations #vector-analysis #tensors #vector-fields
41
Views

Which indices go where in the resulting delta function

Published on
#matrices #vectors #tensors #kronecker-delta
282
Views

Einstein field equation derivation

Published on
#physics #tensors #general-relativity
65
Views

How can I prove the following relation from tensor calculus?

Published on
#vector-spaces #tensors #jacobian #kronecker-symbol #kronecker-delta
79
Views

Coordinate Transformation Law (Tensors)

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#linear-algebra #tensors
52
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How to take the determinant of a rank(1,1) tensor?

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#determinant #tensors #calculus-of-variations #symmetry #jacobian

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