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In the paper, the split quaternion matrix equation AXAη*=B is considered, where the operator Aη* is the η‐conjugate transpose of A, where η∈{i,j,k}. We propose some new real representations, which… Click to show full abstract
In the paper, the split quaternion matrix equation AXAη*=B is considered, where the operator Aη* is the η‐conjugate transpose of A, where η∈{i,j,k}. We propose some new real representations, which well exploited the special structures of the original matrices. By using this method, we obtain the necessary and sufficient conditions for AXAη*=B to have X=±Xη* solutions and derive the general expressions of solutions when it is consistent. In addition, we also derive the general expressions of the least squares X=±Xη* solutions to it in case that this matrix equation is not consistent.
Journal Title: Mathematical Methods in the Applied Sciences
Year Published: 2019
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