Spectral and weak polynomial completeness for the product of nonsingular matrices

Iglésias, Laura; Silva, Fernando C.

http://hdl.handle.net/10400.21/6003

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Authors

Iglésias, Laura

Silva, Fernando C.

Abstract(s)

Let 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).

Keywords

Eigenvalues Characteristic polynomial Invariant polynomials Factorization of matrices

URI

http://hdl.handle.net/10400.21/6003

Citation

IGLÉSIAS, 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.