A generalization of the complex Autonne–Takagi factorization to quaternion matrices

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A real quaternion matrix equation with applications (2013, background): “Following Horn and Zhang’s recent research on -Hermitian matrices (A generalization of the complex AutonneTakagi factorization to quaternion matrices, Linear Multilinear Algebra, DOI:10.1080/03081087.2011.618838), we consider a real quaternion matrix equation involving -Hermicity, i.e. A1Xþ ðA1XÞ þ ”
Two special kinds of least squares solutions for the quaternion matrix equation AXB+CXD=E (2012, unknown): “[6, 18] A matrix A ∈ Qn×n is η-Hermitian if A = A, and a matrix A ∈ Qn×n is η-anti-Hermitian if A = −A, where A = −ηAHη, η ∈ {i, j, k}.”
The η-bihermitian solution to a system of real quaternion matrix equations (2014, methodology): “Recently, Horn and Zhang [2] provided an analogous special singular value decomposition for η-Hermitian matrices.”
The general $\phi$-Hermitian solution to mixed pairs of quaternion matrix Sylvester equations (2017, methodology): “η-Hermitian matrix was first proposed in [35], and further discussed in [17].”