# 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.

194 questions
0answers
28 views

### Is this matrix notation correct?

I have a bunch of matrices that I denote as follows: $$\mathbf{A_j}=(a_{c,k}^j)\in[0,1]^{d\times q}$$ The reason I don't use a tensor of order $3$ is because $d$ will vary for each $j$, which is why ...
1answer
24 views

### d’Alembert Lagrangian for second rank tensors

Consider the Lorentz scalar Lagrange density $$\mathcal{L}=\eta^{\mu\nu}\partial_\mu T^{\alpha\beta}\partial_\nu T_{\alpha\beta}$$ for a second rank tensor whose contravariant and covariant ...
1answer
16 views

0answers
13 views

### Specific, Index-Notation Formula of the determinant of 2-dimensional matrices

I was practicing some old tensor calculus exams and had to answer this question (paraphrased, it has multiple subquestions): If $\eta_{ij}$ is the component of the metric $H$ on a 2D Riemannian ...
0answers
18 views

### Multivariate Gaussian distribution notation

Is the following correct? The prior distribution is a multivariate Gaussian distribution defined as: \begin{equation} \boldsymbol {\mathrm {\theta}}_i \sim \mathcal{MVN}( \boldsymbol {\mathrm {\mu}},...
1answer
67 views

### Prove derivative of contravariant tensor of rank 1 is a mixed tensor of rank 2

$A^\alpha$ is a given contravariant vector (when $\alpha\in {0,1,2,3}$ a $4$-vector in Minkowski space) I need to show that the derivative $\frac{\partial A^\alpha}{\partial x^\beta}$ is a mixed ...
1answer
70 views

### How do multi-indices work, step by step?

Never used multi-indexed summations in my life, neither has anyone else I know. https://en.wikipedia.org/wiki/Multinomial_theorem does not define an upper index for the multi-indexed sum, which ...
1answer
23 views