Explicit formulas and determinantal representation for η-skew-Hermitian solution to a system of quaternion matrix equations | Zendy

Abdur Rehman | Zendy; Ivan Kyrchei | Zendy; Ilyas Ali | Zendy; Muhammad Akram | Zendy; Abdul Shakoor | Zendy

Open Access

Explicit formulas and determinantal representation for η-skew-Hermitian solution to a system of quaternion matrix equations

Author(s) -

Abdur Rehman,

Ivan Kyrchei,

Ilyas Ali,

Muhammad Akram,

Abdul Shakoor

Publication year - 2020

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil2008601r

Subject(s) - mathematics , quaternion , hermitian matrix , noncommutative geometry , representation (politics) , matrix (chemical analysis) , skew , coefficient matrix , rank (graph theory) , matrix representation , pure mathematics , square matrix , algebra over a field , mathematical analysis , combinatorics , symmetric matrix , geometry , eigenvalues and eigenvectors , materials science , physics , organic chemistry , chemistry , quantum mechanics , astronomy , politics , political science , law , composite material , group (periodic table)

Some necessary and sufficient conditions for the existence of the ?-skew-Hermitian solution quaternion matrix equations the system of matrix equations with ?-skew-Hermicity, A1X = C1, XB1 = C2, A2Y = C3, YB2 = C4, X = -X?*; Y=-Y?*, A3XA?*3 + B3YB?*3=C5, are established in this paper by using rank equalities of the coefficient matrices. The general solutions to the system and its special cases are provided when they are consistent. Within the framework of the theory of noncommutative row-column determinants, we also give determinantal representation formulas of finding their exact solutions that are analogs of Cramer?s rule. A numerical example is also given to demonstrate the main results.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research