Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some results on the generalized inverse of tensors and idempotent
  tensors   Let $\mathcal{A}$ be an order $t$ dimension $m\times n\times \cdots \times n$
tensor over complex field. In this paper, we study some {generalized inverses}
of $\mathcal{A}$, the {$k$-T-idempotent tensors} and the idempotent tensors
based on the general tensor product. Using the tensor generalized inverse, some
solutions of the equation $\mathcal{A}\cdot x^{t-1}=b$ are given, where $x$ and
$b$ are dimension $n$ and $m$ vectors, respectively. The {generalized inverses}
of some block tensors, the eigenvalues of {$k$-T-idempotent tensors} and
idempotent tensors are given. And the relation between the generalized inverses
of tensors and the $k$-T-idempotent tensors is also showed.

26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys