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Convertible Subspaces of Hessenberg-Type Matrices

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We describe subspaces of generalized Hessenberg matrices where the determinant is convertible into the permanent by affixing ± signs. An explicit characterization of convertible Hessenberg-type matrices is presented. We conclude that convertible matrices with the maximum number of nonzero entries can be reduced to a basic set.

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Determinant Permanent Hessenberg matrix Convertible matrix

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