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How to decide whether an equation in index notation is valid.

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What is the divergence of $\frac{\vec{r} (\vec{r}.\vec{a})}{r^3}$?

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#calculus #proof-verification #vector-analysis #spherical-coordinates #index-notation
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Proof trace of tensor matrix is invariant to rotation of the axis

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#linear-algebra #rotations #tensors #trace #index-notation
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When to relabel dummy variables in tensor index notation

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#tensor-products #cross-product #index-notation
580
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proof of a fluid dynamics identity using index notation

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#vector-analysis #fluid-dynamics #index-notation
154
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A Problem with Index Notation

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#index-notation
408
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Derivative in Vector vs Index Notation

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#multivariable-calculus #vectors #matrix-calculus #index-notation
63
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Question about tensors

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#riemannian-geometry #tensors #index-notation
28
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Concisely expressing the derivative over a summation

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#summation #partial-derivative #self-learning #index-notation
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Rotation matrix: "sum of squared elements along a row/column is unity: dot product of two different rows is zero"?

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#linear-algebra #matrices #vector-analysis #rotations #index-notation
312
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Convert expression from index to matrix/vector notation

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#matrix-calculus #index-notation
270
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Question on Einstein Summation convention evaluating certain expression

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#index-notation
269
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Matrix manipulations with Levi-Civita symbol

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#matrices #differential-geometry #determinant #inverse #index-notation
45
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Help with understanding indices for Navier Stokes Equation

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#fluid-dynamics #index-notation
103
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Product of a specific $(0,2)$ and $(2,0)$ tensor (Minkowski Metric tensor)

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#tensors #index-notation

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