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- Convertible Subspaces of Hessenberg-Type MatricesPublication . Cruz, Henrique F. Da; Rodrigues, Ilda Inácio; Serôdio, Rogério; Simões, A. M.; Velhinho, JoseWe 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.