JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (11): 97-104.doi: 10.6040/j.issn.1671-9352.0.2020.424

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Representation of matrices and its applications to entropy

ZHAO Ya-qi, REN Fang-guo*   

  1. School of Mathematics and Statistics, Shaanxi Normal University, Xian 710062, Shaanxi, China
  • Published:2021-11-15

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Abstract: To study the properties about the representation for probabilistic distribution of unitary similarities of a matrix and the applications about the concavity of matrix entropy, some research about block matrix, projection matrix and the concavity of matrix entropy is studied. The probabilistic distribution of unitary similarities of any square matrix, the representation of the probabilistic distribution of unitary similarities for the transformation about a complete set of orthogonal projection matrix of any density matrix and some inequalities of matrix entropy are obtained.

Key words: matrix entropy, concavity of entropy, density matrix, projection matrix, unitary similarity, probability distribution

CLC Number: 

  • O151.21
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