Abstract
A class of matrices, called \(\infty \)-radial matrices (1-radial matrices) whose spectral radius equals their \(\infty \)-norm (1-norm), is proposed in this paper and some theoretical results are established to give several necessary and sufficient conditions of this class of matrices. Then, some properties of this class of matrices are presented. Finally, some applications of this class of matrices in the linear discrete dynamic systems are studied such that the zero solution of the linear discrete dynamic systems is asymptotically stable.
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Acknowledgments
This work was supported by the National Natural Science Foundations of China (11201362, 11601409 and 11271297), the Natural Science Foundations of Shaanxi Province of China (2016JM1009) and the Science Foundation of the Education Department of Shaanxi Province of China (14JK1305). The authors would like to thank the anonymous referees for their valuable comments and suggestions, which actually stimulated this work. The authors would also like to thank Professor Jinyun Yuan for his sincere help.
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Communicated by Jinyun Yuan.
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Zhang, Cy., Luo, S. On matrices having equal spectral radius and some matrix norm. Comp. Appl. Math. 37, 912–921 (2018). https://doi.org/10.1007/s40314-016-0375-z
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DOI: https://doi.org/10.1007/s40314-016-0375-z