# Questions tagged [index-notation]

For questions about index notations, e.g. abstract index notation, Einstein summation convention, topics in introductive tensor calculus, Levi-Civita Symbol, Kronecker Delta symbol, proofs of vector calculus identities or fluid dynamics formulae using index notation.

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### Abstract index notation - can't understand identity $(dx^{\mu})_aT^b\partial_bv^a=T^b\partial_b[(dx^{\mu})_av^a]$

I'm trying to get familiar with abstract index notation. Came across this identity: $$(dx^{\mu})_aT^b\partial_bv^a=T^b\partial_b[(dx^{\mu})_av^a]=T^b\partial_bv^{\mu}$$ where $T$ and $v$ are vector ...
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### Sum over an index that needs to fulfill a condition

Introduction I have a matrix $V=(v_{ij})_{1\leq i \leq m, 1\leq j \leq n}$ containing integer numbers, representing the number of vehicles. Each $i-$row represents the place of origin of those ...
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### Index Notation - An Inconsistency with a deeper meaning?

Background Suppose we have a linear transformation $T : V \to W$ where $V$ and $W$ are finite dimensional vector spaces with bases $(e_i)$ and $(f_i)$ respectively. Using index notation, it is ...
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### How to write expressions in tensor notation?

I’m a self-taught math student and i want to learn how to work and calculate with tensors. I’m pretty familiar with the theory behind them, but something about the the different notations just does ...
Given a real matrix $F$, I'm trying to simplify the expression $$C_{ijkl} = \frac{\partial (F_{ip}F_{jp})}{\partial F_{km}} F_{lm}$$ One reference I saw online says the right-hand side simplifies to: ...