Least-squares problem for the quaternion matrix equationAXB+CYD=Eover different constrained matrices
S. J. Yuan, Qing‐Wen Wang, Xiang Zhang · International Journal of Computer Mathematics · 2012
For any A=A 1+A 2 j∈Q n×n and η∈ i, j, k , denote A η H =−η A H η. If A η H =A, A is called an $\eta$-Hermitian matrix. If A η H =−A, A is called an η-anti-Hermitian matrix. Denote η-Hermitian matrices and η-anti-Hermitian matrices by η HQ n×n and η AQ n×n , respectively. 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 for the quaternion matrix equation AXB+CYD=E over X∈η HQ n×n and Y∈η AQ n×n .