# Tagged Questions

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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### Can I use symbolic tensors for simple linear algebra and calculus?

As an example, I'd like to calculate this symbolic derivative: $\frac{\partial}{\partial b}(x-A.b)^{\mathsf{T}}.(x-A.b)$ where $x$ and $b$ are vectors and $A$ is a matrix. What I tried is this: ...
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### Efficient way to flatten or transpose-arrayreshape tensors

I have a tensor of dimensions $(2, 100, 100, 2, 100, 100)$ and I want to reshape it to a form of $(2*100*100,2*100*100)$, e.g. Flatten[A,{{1,5,6},{4,2,3}}]. If I ...
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### How to write Coordinate Chart in Xcoba in index form?

I am using xCoba for manipulating tensors. I do the usual, defining my metric, manifold, chart etc. ...
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### Nested TensorContract bug

Bug introduced in version 9.0.0 or 9.0.1 and fixed in 10.1 or 10.2 When nesting TensorContract the result I get is wrong. Input: ...
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### how to associate a metric for tensor contraction operations?

I see that Version 9 now has some built in tensor support (which was missing back when previously asked How to represent and manipulate abstract indexed vector (or tensor) expressions?). The docs ...
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### How to deal with tensor argument in LibraryLink?

For the Bézier surface, which owns the following matrix definition: \begin{align*} \mathbf{S}(u,v)&=\sum_{i=0}^m \sum_{j=0}^n \mathbf{P}_{i,j} B_{i,m}(u) B_{j,n}(v)\\ &=\small \begin{...
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### Simplifying symbolic expressions using TensorExpand

Following my previous question I have this issue using TensorExpand: KroneckerProduct[x, y].(KroneckerProduct[2 z, w]) // TensorExpand results in ...
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### Arrays with two different types of indices

Is there a way of having arrays which have, so to speak, two different depths $m,n$? From the point of view of memory usage, it would be the same as an array of depth $m+n$, but I would like to ...
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### Fast construction and reshaping of large tensors

I'm trying to construct a large matrix which is derived from some higher rank tensor (the rank of interest to me changes case by case, so it needs to be a general method). Currently, the process of ...
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### Finding basis of isotropic tensors of rank r

I am looking for a way to obtain a basis of isotropic tensors of rank $r$. Actually I am mostly interested in rank $8$ isotropic tensors but maybe you know already a simple algorithm in order to ...
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### SymmetrizedArray of stiffness/compliance tensor

The stiffness and compliance tensors of a material are 3x3x3x3 tensors relating stress and strain. ...
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### Derivative with respect to a tensor

I am trying to differentiate a tensor with respect to another one in Mathematica, but I can't do it. Down below is the code I am using: ...
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### How does TensorReduce use assumptions?

I would like to use TensorReduce by assuming that certain patterns of functions are tensors. From documentation of TensorReduce: ...
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### Scalar from tensor contraction

I'm trying to calculate the Kretschmann scalar in mathematica, it is given by: $c = R^{abcd} R_{abcd}$ Where $R^{abcd}$ is the Riemann tensor. I'm following this MSE post so I modified it to ...