Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on matrices mapping a positive vector onto its element-wise
  inverse   For any primitive matrix $M\in\mathbb{R}^{n\times n}$ with positive diagonal
entries, we prove the existence and uniqueness of a positive vector
$\mathbf{x}=(x_1,\dots,x_n)^t$ such that
$M\mathbf{x}=(\frac{1}{x_1},\dots,\frac{1}{x_n})^t$. The contribution of this
note is to provide an alternative proof of a result of Brualdi et al. (1966) on
the diagonal equivalence of a nonnegative matrix to a stochastic matrix.

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The categories of this paper are: physics
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th