Iglésias, LauraSilva, Fernando C.2016-04-152016-04-152015-10-03IGLÉSIAS, LAURA; SILVA, FERNANDO C.; - Spectral and weak polynomial completeness for the product of nonsingular matrices. Linear and Multilinear Algebra. ISSN.0308-1087. Vol. 63, N.º 10, SI (2015), pp. 1937-1946.0308-10871563-5139http://hdl.handle.net/10400.21/6003Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F, satisfying the following property: for every monic polynomial f (x) = x(n) + a(n-1)x(n-1) +... + a(1)x + a(0) over F, with a root in F and a(0) = (-1)(n) det(AB), there are nonsingular matrices X, Y is an element of F-nxn such that XAX(-1)Y BY-1 has characteristic polynomial f (x).engEigenvaluesCharacteristic polynomialInvariant polynomialsFactorization of matricesjournal article10.1080/03081087.2013.862620