Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the matrix $pth$ root functions and generalized Fibonacci sequences   This study is devoted to the polynomial representation of the matrix $p$th
root functions. The Fibonacci-H\"orner decomposition of the matrix powers and
some techniques arisen from properties of generalized Fibonacci sequences,
notably the Binet formula, serves as a triggering factor to provide explicit
formulas for the matrix $p$th roots. Special cases and illustrative numerical
examples are given.

13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin