# Questions tagged [tensors]

Use this tag for questions that involve tensors. Tensors are fundamental tools for linear computations, generalizing vectors and matrices to higher ranks. Mathematica 9 introduces powerful methods to algebraically manipulate tensors with any rank and symmetry.

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### In simple terms, what is a Tensor Space? [closed]

I've heard of tensor spaces, and they sound intriguing to my non-mathematically educated mind. I was wondering if anyone could give a, "Tensor Space for Dummies," rundown. If not possible to ...
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### Best way to work with Tensor Networks

I have to write a script in which I have to work with a very simple tensor network but I can't find a nice scalable way to make this work. The basic object I am working with is a tensor more or less ...
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### LeviCivitaTensor contraction indices

My computer has problems when I try to perform a calculation with TensorContract. In particular, with the second answer to my previous question Contracting indices ...
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### Optimising tensor operations under memory constraints

Let riem is a free variable with riem ∈ Arrays[{4, 4, 4, 4} as assumption. Let: ...
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### Contracting indices in lists

Using an answer to this question (Working with Dirac Gamma Matrices using FeynCalc - A simple problem), I defined ...
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### Expanding Determinant as Multilinear Alternating Function

I am working with the expression $$\det\big{|}f(-kx), f(-(k-1)x),\cdots,f(0),\cdots, f((k-1)x), f(kx), g(x)\big{|},$$ where $f,g\colon\mathbb{R}\mapsto \mathbb{R}^{2k+2}$, and want to use the Taylor ...
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### Does Solve work with symbolic tensors?

I am considering the usefulness of Mathematica's symbolic tensors to handle algebra which I encounter in acoustics of solids. Is there a way to solve equations written in symbolic tensors? This is ...
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### How to state nontrivial tensor symmetry assumptions?

For example dddg, the third derivative of the metric tensor, in dimension $4$. I need to state that it is symmetric in the first two indices and symmetric in the ...
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### Hypothetical aplication of rules/restricting rules to a given context?

I have the code TensorDimensions[TensorContract[c, {{1, 2}}]]. It is in normal form. But if I add the rules: ...
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### Correct syntax for tensor operators?

So I have an operator $A_0$ whose matrix representation is given by $$A_0 = \begin{pmatrix} 0 & -i \\ -i & 0\end{pmatrix},$$ and I also have two vector states $|0\rangle$ and $|1\rangle$ ...
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### Fourth Order Tensor rotation [duplicate]

What is the easiest way to perform Rotation for Higher Order Tensors in Mathematica ? For Instance 4th order tensor $C_{ijkl} = \lambda_{im}\lambda_{jn}\lambda_{ko}\lambda_{lp} C_{mnop}$
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### speed up tensor expand

I am using the following code ...
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### A simple problem on TensorTranspose

In the "Applications" part of TensorTranspose, it is given an example on the calculation of Christoffel according to metrics. I am confused about the definition of <...
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### How to reproduce this tensor calculation with Mathematica [closed]

The tensor operation shown in the red box is used in the textbook(P117-P120) to prove that there are only 9 independent constants for orthotropic materials: I want to use MMA to reproduce the ...
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### How to use Mathematica to show why engineering strain is not a tensor [closed]

One of the most classical examples in the mechanics of materials is that engineering strain is not tensor. I want to use Mathematica to show why it doesn't meet the tensor requirements. ...
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### How to implement Einstein summation convention with differential operators

Statement of this problem: In the textbook, the following differential equilibrium equations can be expressed by tensors: Using Einstein's summation convention, the formula in the figure above can be ...
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### Calculate dot product of two tensor products in mathematica as tensorproduct

I would like to calculate (\mathbb{1} \otimes \mathbb{1} \otimes \sigma^+)(\mathbb{1} \otimes \mathbb{1} \otimes \sigma^-) = (\mathbb{1} \otimes \mathbb{1} \otimes \left( \begin{array} \\ 1 &0 ...
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### What should I do to get a fourth-order tensor with only two independent components

I see this example in help SymmetrizedIndependentComponents, We can see that matrix A has only four independent components: <...
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### How to prove that isotropic materials have only two independent constants by tensor operation rules [duplicate]

I want to use tensor method to prove that there are only two independent elastic constants for isotropic materials. But I can' t get two independent results after reading related posts. The following ...
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### Determinant of the tensor matrix in Mathematica? [closed]

I have a data: As an example, it looks like this: Then, when I try to take Det[]: How we can find determinant value of these kind of matrices ?
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### Spin Connection using Mathematica

Hello I want to use Mathematica in order to calculate the spin connection of a metric, specifically of the metric \begin{equation} \left(\begin{array}{cccc} -1 & 0 & 0 & 0 \\ 0 & \...
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### Tensor contraction

How do I let mathematica compute a tensor contraction like $\delta_{ab}\delta_{bc}$ with an output $\delta_{ac}$ efficiently? I tried TensorContract and TensorReduce but they were not helpful. ...
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### How do I apply assumptions to a table of functions

I have a table, really its a tensor but anyways I would like to apply an assumption to it, i.e. 1 - 2 phi[t,x,y,z] == 1 and have it print the tensor after it has ...
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### Use Mathematica to draw a tensor-like network

What are the Mathematica ways to draw this seemly delicate figure? Such that we can output a PDF file in the end.