A real representation of complex polynomial matrices in the framework of conjugate product

ABSTRACT

A real representation of complex polynomial matrices in the framework of conjugate product is first proposed, and some interesting properties of the proposed real representation are given. With the real representations as tools, alternative proofs for some properties of conjugate product are given. In addition, the concept of real determinant is proposed for complex polynomial matrices in the framework of conjugate product, and based on the real determinant the invertibility in the framework of conjugate product is investigated. These results imply that the proposed real representation has potential applications in the further investigation of conjugate product.

Keywords:

• Real representation
• conjugate product
• real determinant
• polynomial matrices
• invertible matrices

2000 MSC SUBJECT CLASSIFICATION:

• 11C08

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Shenzhen Municipal Basic Research Project for Discipline Layout with Project Number JCYJ20170413112722597, the National Natural Science Foundation of China [Grant Number 61603111 and 61773387], and Shenzhen Municipal Projects for Basic Research with Project Number JCYJ20170307150227897.