This paper considers a completion problem of a nonsingular block matrix over the real quaternion algebra : Let be nonnegative integers, , and be given. We determine necessary and sufficient conditions so that there exists a variant block entry matrix such that is nonsingular, and is the upper left block of a partitioning of . The general expression for is also obtained. Finally, a numerical example is presented to verify the theoretical findings.
"Completing a Block Matrix of Real Quaternions with a Partial Specified Inverse." J. Appl. Math. 2013 (SI03) 1 - 5, 2013. https://doi.org/10.1155/2013/271978