Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On some properties of three different types of triangular blocked
  tensors   We define three types of upper (and lower) triangular blocked tensors, which
are all generalizations of the triangular blocked matrices. We study some basic
properties and characterizations of these three types of triangular blocked
tensors. We obtain the formulas for the determinants, characteristic
polynomials and spectra of the first and second type triangular blocked
tensors, and give an example to show that these formulas no longer hold for the
third type triangular blocked tensors. We prove that the product of any two
$(n_1,\cdots,n_r)$-upper (or lower) triangular blocked tensors of the first or
second or third type is still an $(n_1,\cdots,n_r)$-upper (or lower) triangular
blocked tensor of the same type. We also prove that, if an
$(n_1,\cdots,n_r)$-upper triangular blocked tensor of the first or second or
third type has a left $k$-inverse, then its unique left $k$-inverse is still an
$(n_1,\cdots,n_r)$-upper triangular blocked tensor of the same type. Also if it
has a right $k$-inverse, then all of its right $k$-inverses are still
$(n_1,\cdots,n_r)$-upper triangular blocked tensors of the same type. By
showing that the left $k$-inverse (if any) of a weakly irreducible nonsingular
$M$-tensor is a positive tensor, we show that the left $k$-inverse (if any) of
a first or second or third type canonical $(n_1,\cdots,n_r)$-upper triangular
blocked nonsingular $M$-tensor is an $(n_1,\cdots,n_r)$-upper triangular
blocked tensor of the same type all of whose diagonal blocks are positive
tensors. We also show that every order $m$ dimension $n$ tensor is permutation
similar to some third type normal upper triangular blocked tensor (all of whose
diagonal blocks are irreducible). We give an example to show that this is not
true for the first type canonical upper triangular blocked tensor.

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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org