Algebraic Characterizations of Relationships between Different Linear Matrix Functions

Yongge Tian () and Ruixia Yuan
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Yongge Tian: Shanghai Business School, College of Business and Economics, Shanghai 201400, China
Ruixia Yuan: Shanghai Business School, College of Business and Economics, Shanghai 201400, China

Mathematics, 2023, vol. 11, issue 3, 1-19

Abstract: Let f ( X 1 , X 2 , … , X k ) be a matrix function over the field of complex numbers, where X 1 , X 2 , … , X k are a family of matrices with variable entries. The purpose of this paper is to propose and investigate the relationships between certain linear matrix functions that regularly appear in matrix theory and its applications. We shall derive a series of meaningful, necessary, and sufficient conditions for the collections of values of two given matrix functions to be equal through the cogent use of some highly selective formulas and facts regarding ranks, ranges, and generalized inverses of block matrix operations. As applications, we discuss some concrete topics concerning the algebraic connections between general solutions of a given linear matrix equation and its reduced equations.

Keywords: block matrix; general solution; generalized inverse; matrix equation; matrix expression; range; rank (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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