Estimate for the lower bound of rank and the upper bound of eigenvalues norms' sum of given quaternion matrix

  • Authors:

  • Junliang Wu;Yan Zhang

  • Affiliations:

  • College of Mathematics and Physics, Chongqing University, Chongqing, 400044, China;College of Mathematics and Physics, Chongqing University, Chongqing, 400044, China

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2010

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Abstract

This work is concerned with estimating the lower bound of rank for a given quaternion square matrix, rectangular matrix or normal matrix, and estimating the upper bound for the sum of the eigenvalue norms of a given quaternion matrix. A sufficient condition is provided to confirm whether a given quaternion matrix is nonsingular. It sharpens some results due to Tu Bo-xun and Semyon Aranovich Gerschgorin and Schur, respectively. Some examples are provided to show the effectiveness of our results.