# 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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### Efficient tensor product followed by contraction [duplicate]

Say I want to efficiently evaluate $\sum_{kl}A_{ikjl}B_{kl}$ where $A$, $B$ are numerical tensors. This has been discussed before but with no focus on efficiency. A straightforward way as mentioned ...
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### Inverse KroneckerProduct given other arguments

I'm having problems working out how to do the inverse of a two argument Kronecker Product, given one of the decomposed column vectors. For example, say I have used the Kronecker Product on two ...
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### How can I define or use a new coordinate system in Mathematica?

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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### 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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### SymmetrizedArray of stiffness/compliance tensor

The stiffness and compliance tensors of a material are 3x3x3x3 tensors relating stress and strain. ...
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### How to take derivative of a tensor leading to kronecker delta? [duplicate]

I'm trying to write a Mathematica program to find derivatives such as the following simple example: Could you please help?
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### Change of basis for a rank 3 Cartesian tensor

I have a Cartesian tensor $\chi_{ijk}$ and I want to express the elements in terms of a new basis to get $\chi_{ijk}^\prime$. The transformation is represented using $a_{ij}$. The tensor transforms ...
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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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### Solving a System/Matrix of Equations in Matrix Form

Ok, I am trying to solve an equation involving matrices (well, tensors actually), which is of the form: $\mathbf{e}^{T} \cdot \mathbf{M} \cdot \mathbf{e}$ = $\mathbf{N}$, where $\mathbf{e}$ is an ...
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### How to put the tensor product of two operators onto two variables?

I am trying to make an intuitive Mathemtaica program to show the principle of quantum walking. The idea of quantum walking is very simple and direct, but when I try to transfer it into Mathemitca ...
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### Sum with Levi-Civita [duplicate]

I'm trying to write the expression $$\sum_{\alpha,\beta = 1}^{4}\epsilon_{\mu \nu\alpha\beta}a^{\nu} b^{\alpha} c^{\beta}$$ in Mathematica, where $\epsilon$ is the Levi-Civita symbol and $a$, $b$, $c$ ...
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### Mathematica package for supergravity and superstring theory

I am looking for a Mathematica package that can manipulate tensors for supergravity, string theory or M-theory. I am particularly looking for a package that can do spinor and Clifford algebra ...
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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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### Tensor product involving Levi Civita symbol [duplicate]

I'm working with xAct package. I've defined the tensor component values and my issue is that I want an expression involving Levi Civita symbols and tensor components, I don't know how to deal with it. ...
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### Get rid of external library dependency [closed]

I am trying to generate C code for some functions, which I do not post in full because they are a few hundred lines long. The functions do nothing too fancy: a bunch of dot products, powers and roots. ...
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### How to get rid of nested matrices

If I type into Mathematica TensorProduct[IdentityMatrix[2],IdentityMatrix[2]] It gives me a result that has nested matrices. How do I turn that into a normal ...
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### How to select elements in a tensor conditional upon their indices

I have a tensor, u, of rank one, meaning that I have a matrix whose elements are themselves matrices. I would like to select, and make a list of, only those sub-matrices whose indices comply with the ...
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### Defining tensor components generally

I would like to define a tensor according to its components, something like the following: [F(x)]_i,j = Integrate[f(x,y)A_i(y)B_j(y),y] where i and j are ...
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### Matrix/tensor addition behaving funny under replacement?

I have two matrices I want to add, and one of the matrices is a tensor product of two vectors. I've used a SetDelayed to define the summed matrix, because I want to evaluate it for different values of ...
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### How to take derivative of parameterized coordinate?

Suppose I have a vector in $\mathbb{R}^n$ but $n$ is not known in advance. I want to be able to write functions which operate on the components of that vector, and then I'd like to be able to take ...
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### Why TensorReduce not working here?

I would like to use TensorReduce to work on the tensor contraction $y_{ib}y_{ia}$ (where index $i$ is summed). However, ...
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### How to faster map density matrix element to make differential equations

I have a time dependent matrix $M(t)$ of $L^n \times L^n$ size and want to write differential equations like D[M[i,j][t],t] = H[i,j][t] Here is my code: ...
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### Evaluating the tensor product many times for a given list

I need to evaluate the tensor product 10 times in a given list( {g,e,r}) Here I have evaluated for 3 times... ...
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### Why the tensor product of list of variable change the subscript position in products

{Subscript[g, 1],Subscript[e, 1]}\[TensorProduct]{Subscript[g, 2],Subscript[e, 2]}\[TensorProduct]{Subscript[g, 3],Subscript[e, 3]} I am expecting answer like ... ...
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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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### Linearized Einstein Equations with Mathematica

I need to compute the linearised Einstein Equations around a fixed metric $g_{\mu \nu}$ which is not the flat metric. Someone knows any Mathematica package or a review that can help me?
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### How to apply a tensor to a list of arguments

The problem I have is the following: Let C be a list of coordinates, say, C = {x1, x2, ..., xn} and ...