Sums of Alternating Matrices and Invertible Matrices
نویسندگان
چکیده
A square matrix is said to be alternating-clean if it is the sum of an alternating matrix and an invertible matrix. In this paper, we determine all alternating-clean matrices over any division ring K. If K is not commutative, all matrices are alternating-clean, with the exception of the 1× 1 zero matrix. If K is commutative, all matrices are alternating-clean, with the exception of odd-size alternating matrices, and six special 2× 2 matrices in the case where K is F2, the field of two elements. Similar results are obtained over semilocal rings.
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