# 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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### InternalBag inside Compile

Since InternalBag, InternalStuffBag and InternalBagPart can be compiled down, it is a ...
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### How to calculate scalar curvature, Ricci tensor and Christoffel symbols in Mathematica?

I am seeking a convenient and effective way to calculate such geometric quantities. I've used packages like TensoriaCalc, but they don't work at all time. Sometimes,...
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### What is the definition of Curl in Mathematica?

I have a usual mathematical background in vector and tensor calculus. I was trying to use the differential operators of Mathematica, namely Grad, ...
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### Nearest Kronecker Product

Some people (see The ubiquitous Kronecker product by Van Loan) have worked on finding two matrices $\mathbf A$,$\mathbf B$ of specified size whose tensor product $\mathbf A\otimes\mathbf B$ is closest ...
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### Higher order SVD

Does anyone know how to do a higher order SVD in Mathematica ? A good reference seems to be here http://www.sandia.gov/~tgkolda/pubs/pubfiles/SAND2007-6702.pdf but I don't understand their formalism ...
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### Using Mathematica for tensor analysis

Has anybody used tensors in Mathematica? How to properly work with them? I find Mathematica not very friendly in this field, as I am defining my own functions for lowering & raising indices, ...
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### Ways to compute inner products of tensors

One way to evaluate the following sums is combining Table and Sum: $u_{abcd} = \sum_{e=1}^3 v_{aeb}w_{ced}$ $q_{ab} = \sum_{d,e=1}^3 v_{d e a}w_{deb}$ It will look like ...
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### How can I define or use a new coordinate system?

I want to use the dipole coordinate system as defined in this paper: http://arxiv.org/abs/physics/0606044 I see that Mathematica can do all kinds of vector analysis using different kinds of ...
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### Python's einsum equivalent in Mathematica?

Python's numpy has einsum function, which allows to express wide range of combinations of ND-arrays multiplications, transposings, convolutions etc in one short ...
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### inverse of abstract matrix

If you assume the matrix $A$ is invertible, then $A^{-1} \cdot A = I$. Is there an assumption for invertibility in Mathematica 9? How can one make the following evaluate to the identity matrix $I_3$? ...
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### Nice use case for symbolic tensors?

I come from before the times of symbolic tensors in Mathematica, and am used to working with concrete tensors and custom commands to contract them using Transpose, Dot, etc. I recently realized that ...
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### Verifying and deriving basic (block) matrix identities

How can I use the new symbolic matrix/tensor capabilities to verify matrix identities, such as (1) or (2) Even better, how can I ask Mathematica to derive expressions for X, Y, Z, and U like ...
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### Performance improvements by using Activate and Inactivate

In a question about improving performance of a TensorContract of a TensorProduct, user jose suggested replacing ...
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### How can I "multiply" nested lists?

Given two nested lists alist={{a,b,c},{d,e,f}} blist={{r,s,t},{x,y,z}} How can I get ...
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### Equivalent of numpy's newaxis

Numpy has a newaxis object that allows you to insert a new dimension of length 1 into an array. So after ...
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### Compute covariant derivative in Mathematica

I need to compute covariant derivatives in Mathematica. Searching online I just found the package "Ricci" which only does symbolic computations: I instead need to do actual computations. This is ...
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### What is the best source to learn how to use tensor operations (exterior algebra) in Mathematica?

I'm specifically interested in the TensorProduct,TensorWedge, HodgeDual and certain build in functions to do tensor arithmetic like TensorReduce, TensorExpand. I would like to do exterior algebra ...
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### Error messages from TensorContract and TensorReduce

I am struggling with a few errors when using symbolic tensors. I am using mathematica 9.0.1.0, linux x86. The following code generates what seems to me an incorrect tensor, this is the smallest ...
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