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Level-m scaled circulant factor matrices over the complex number field and the quaternion division algebra

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Abstract

The level-m scaled circulant factor matrix over the complex number field is introduced. Its diagonalization and spectral decomposition and representation are discussed. An explicit formula for the entries of the inverse of a level-m scaled circulant factor matrix is presented. Finally, an algorithm for finding the inverse of such matrices over the quaternion division algebra is given.

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Author information

Correspondence to Zhao-Lin Jiang.

Additional information

Foundation item: the National Natural Science Foundation of China (69972036)

Jiang Zhaolin1,2 received his BS and MS from Qufu Normal University in 1986 and 1993, respectively. Since 1986 he has been at the Linyi Teachers College. Since 2000 he has been at the Xidian University for Ph.D. His research interests focus on the numerical linear algebra and matrix theory.

Liu Sanyang1 received his BS and MS and Ph.D from Shaaxi Normal University and Xidian University and Xi'an Jiaotong University in 1982 and 1984 and 1989, respectively. Since 1987 he has been at the Xidian University. His research interests focus on the multiobjective programming, combinatorial optimization, convex analysis and matrix theory.

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Jiang, Z., Liu, S. Level-m scaled circulant factor matrices over the complex number field and the quaternion division algebra. JAMC 14, 81–96 (2004). https://doi.org/10.1007/BF02936100

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AMS Mathematics Subject Classification

  • 15A21
  • 65F15

Key words and phrases

  • Level-m scaled circulant factor matrix
  • diagonalization
  • spectral decomposition
  • inverse
  • quaternion division algebra