2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221520Amitsur's formula, which expresses det(A+B) as a polynomial in coefficients of the characteristic polynomial of a matrix, is generalized for partial linearizations of the pfaffian of block matrices. As applications, in upcoming papers we determine generators for the SO(n)-invariants of several matrices and relations for the O(n)-invariants of several matrices over a field of arbitrary characteristic.27 pages; v3. Now numeration of statements in this preprint is the same as in the corresponding paperRings and Algebras15A15text