The least squares η-Hermitian problems of quaternion matrix equation AHXA + BHYB=C | Zendy

S. J. Yuan | Zendy; QingWen Wang | Zendy; Zhiping Xiong | Zendy

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The least squares η-Hermitian problems of quaternion matrix equation AHXA + BHYB=C

Author(s) -

S. J. Yuan,

QingWen Wang,

Zhiping Xiong

Publication year - 2014

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/fil1406153y

Subject(s) - hermitian matrix , mathematics , quaternion , kronecker product , matrix (chemical analysis) , real representation , hermitian function , pure mathematics , algebra over a field , combinatorics , kronecker delta , physics , geometry , irreducible representation , chemistry , chromatography , quantum mechanics

For any A=A1+A2j?Qnxn and ?? {i,j,k} denote A?H = -?AH?. If A?H = A,A is called an ?-Hermitian matrix. If A?H =-A,A is called an ?-anti-Hermitian matrix. Denote ?-Hermitian matrices and ?-anti-Hermitian matrices by ?HQnxn and ?AQnxn, respectively. In this paper, we consider the least squares ?-Hermitian problems of quaternion matrix equation AHXA+ BHYB = C by using the complex representation of quaternion matrices, the Moore-Penrose generalized inverse and the Kronecker product of matrices. We derive the expressions of the least squares solution with the least norm of quaternion matrix equation AHXA + BHYB = C over [X,Y] ? ?HQnxn x ?HQkxk, [X,Y] ? ?AQnxn x ?AQkxk, and [X,Y] ? ?HQnxn x ?AQkxk, respectively.

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