摘要
In this paper,the concepts of con-numbers and con-matrices are proposed by the introduction of conjugate operators into the field of complex numbers,and some properties of these two concepts are derived.In addition,two potential applications of these two concepts are addressed in details.Specifically,a class of quantum systems is expressed in terms of the proposed con-numbers,and the R-linear mapping is represented by con-matrices.These two applications imply the importance of the con-numbers and con-matrices.In addition,some methods are discussed on the construction of the conjugate-operator-induced numbers.Also,some further research directions are provided on these extended numbers and matrices with their applications to systems control.
基金
supported by the National Natural Science Foundation of China for Excellent Young Scholars under Grant No.61822305
Major Program of National Natural Science Foundation of China under Grant Nos.61690210 and 61690212
the Fundamental Research Funds for the Central Universities under Grant No.HIT.BRETIV.201907
Shenzhen Municipal Basic Research Project for Discipline Layout with Project No.JCYJ20180507183437860
Guangdong Natural Science Foundation under Grant Nos.2020A1515011091 and 2019A1515011576。
