The kronecker product and its application

Document Type : Research Paper

Authors

University of Qom

Abstract

The Kronecker product of two matrices, denoted by $ A\otimes B $, possesses interesting properties that have led to its extensive use in various fields such as signal processing, image processing, and quantum computations. This multiplication preserves properties such as invertibility, orthogonality, triangularity, symmetry, and many others. If $ A $‎ is a matrix of zeros and ones or an adjacency matrix of a graph, the powers of its Kronecker product result in the generation of fractals or Kronecker product graphs. Another highly practical application is in solving matrix equations like Sylvester equations $ AX+XB=C $‎ and Lyapunov equations $ AX+XA=H $. This article aims to familiarize the reader with some properties of the Kronecker product. Additionally, it briefly describes some of its applications in fast transforms, graphs, fractals, random self-avoiding walks, matrix equations, and matrix decompositions.

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References

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History

  • Receive Date: 26 May 2017
  • Revise Date: 16 January 2018
  • Accept Date: 16 January 2018
  • Publish Date: 22 May 2018

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