12 questions linked to/from Ways to compute inner products of tensors
1k views

### 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 ...
41 views

### Rotating a 4th-dimension Array of symbolic variables [duplicate]

I am looking to rotate a 4th dimension array C[i,j,k,l] using a rotation matrix Q[i,j]. I already know how this is done in 3x3 matrices (Q.A.Transpose[Q]) but I am having a hard time doing it for a ...
5k views

### Flatten command: matrix as second argument

One thing I could never wrap my head around is how Flatten works when provided with a matrix as the second argument, and the Mathematica help isn't particularly ...
2k views

### Use Mathematica as a terminal

I love how notebooks work in Mathematica. You can edit code in real time and hit Ctrl+Shift to run it. Additionally you copy and paste different cells around to organize and test ideas. Search ...
1k views

### How to efficiently compute the partial trace of a matrix?

How can we efficiently compute the partial trace of a matrix with Mathematica? There is some Mathematica code around to compute this, but most of it seems outdates and not very well written. See for ...
762 views

### Matrix multiplication that includes a tensor

How would I best express the following in Mathematica: $\begin{pmatrix}2 & 4\end{pmatrix} \begin{pmatrix}r_1 & r_2\\r_3 & r_4\end{pmatrix} \begin{pmatrix}6 \\ 8\end{pmatrix}$, where $r_i$ ...
821 views

### 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 ...
376 views

### The fastest way of raising indices of high rank tensor

I have some high dimensional high rank tensors, let's say $$F_{ijkl}$$ and I need to find $$F^{abcd}=g^{ai}g^{bj}g^{ck}g^{dl}F_{ijkl}.$$ Here $g^{ij}$ is the contravariant metric. Simple summation ...
361 views

### Summing tensors in mathematica

How do I perform the following summation in mathematica? $$\Sigma_{m=1}^5 e_{ijklm}A^{mn}$$ I have the $e_{ijklm}$ tensor of rank 5 in 5 dimension as a array and $A^{mn}$ ...
173 views

### Generalized n-fold inner product for tensors, iteration and indexing or built in functions?

I'm very new to Mathematica, and struggling to convert one of the codes I'd written in MATLAB. I am trying to program a function for a generalised inner product between two tensors, that is for ...