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

作者：Wu Junliang^*; Zhang Yan

来源：Computers & Mathematics with Applications, 2010, 59(9): 3160-3166.

DOI：10.1016/j.camwa.2010.02.041

• Quaternion matrix
• Rank
• Lower bound
• Eigenvalue
• Upper bound

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.

• 出版日期2010-5
• 单位重庆大学