Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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DECOMPOSITION OF THE KRONECKER SUMS OF MATRICES INTO A DIRECT SUM OF IRREDUCIBLE MATRICES

  • Gu, Caixing (Department of Mathematics California Polytechnic State University) ;
  • Park, Jaehui (Research Institute of Mathematics Seoul National University) ;
  • Peak, Chase (Department of Mathematics California Polytechnic State University) ;
  • Rowley, Jordan (Department of Mathematics California Polytechnic State University)
  • Received : 2020.05.15
  • Accepted : 2020.12.23
  • Published : 2021.05.31
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Abstract

In this paper, we decompose (under unitary similarity) the Kronecker sum A ⊞ A (= A ⊗ I + I ⊗ A) into a direct sum of irreducible matrices, when A is a 3×3 matrix. As a consequence we identify 𝒦(A⊞A) as the direct sum of several full matrix algebras as predicted by Artin-Wedderburn theorem, where 𝒦(T) is the unital algebra generated by Tand T*.

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Acknowledgement

Jaehui Park was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (Grant No. NRF2018R1A2B6004116).

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