The tensor tag has no usage guidance.

**4**

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143 views

### Obtaining the metric from the mixed Ricci tensor $R^i{}_j$

In chapter 5 of the book "Einstein Manifolds", Arthur Besse discusses the possibility to find the metric $g$ when knowing the Ricci curvature tensor $Ric(g)$ ($=R_{ij}$).
But what do we know about ...

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54 views

### Mixed tensor index position significance

What is the significance of tensor index position?
For example the fourth order Riemann curvature tensor
\begin{align}
R^m_{ijk}
\end{align}
or
\begin{align}
R^{\phantom{i}m}_{i\phantom{m}jk}.
...

**2**

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33 views

### Tensor of Relative Bases

Suppose $U,V,W$ are the cyclotomic fields $\mathbb{Q}(\zeta_{m_3})$, $\mathbb{Q}_(\zeta_{m_2})$, and $\mathbb{Q}(\zeta_{m_1})$ respectively, where $m_1 \mid m_2 \mid m_3$ so that $U/V/W$ is a tower of ...

**2**

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91 views

### Cannot multivectors be classified more easily than general tensors?

This is sort of a spinoff of Is there a useful generalization of the Schmidt decomposition to the tensoring together of 3 or more vector spaces? - seems to be almost hopeless, but maybe some partial ...

**1**

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88 views

### Functional composition of Hadamard product

Let $\Bbb K$ be a ring. Are there universal functions $$f,h:\Bbb K^{n\times n}\times\Bbb K^{n\times n}\times\Bbb K^{n\times n}\times\Bbb K^{n\times n}\rightarrow\Bbb K^{n\times n}$$ $$g:\Bbb ...

**1**

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46 views

### Possibility Of Curvature and/or Mellin based approach to (Non-linear) system Identification?

I have some experience in non-linear system identification (from an experimental point of view) using higher oder spectral analysis. I see this is the most popular way of identifying non-linearities ...

**1**

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100 views

### Null vector fields given Bondi metric

I'm trying to understand how to compute the null future-directed vector fields if I have a given (Bondi) metric
$g=-e^{2\nu}du^{2}-2e^{\nu+\lambda}dudr+r^{2}d\Omega$
with $d\Omega$-standard metric ...

**1**

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276 views

### How to find the tensor product of modules that we don't know a basis for them?

Hi
I know how to calculate some easy tensor products like $\mathbb{Z}/m\mathbb{Z} \otimes_{\mathbb{Z}} \mathbb{Z}/n\mathbb{Z}\cong_{\mathbb{Z}} \mathbb{Z}/(m,n)\mathbb{Z} $ or $F[X] \otimes_{F} F[Y] ...

**1**

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264 views

### tensor/hypermatrix analogues of $GL(n,\mathbb{C})$?

Please excuse me if this question turns out to be incredibly silly for one reason or another.
Are there tensor/hypermatrix analogues of $GL(n,\mathbb{C})$ that are interesting? What I'm mainly ...

**0**

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23 views

### Restrictions of potential tensor fields to toric subgroups

Let $G$ be a compact connected nonabelian Lie group and let $f$ be a symmetric tensor field of order $m\geq1$ on $G$.
Let $T\subset G$ be a translate of a torus subgroup of $G$ with $\dim(T)\geq1$.
...