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- Bounds for the zeros of unilateral octonionic polynomialsPublication . Serôdio, Rogério; Beites, P. D.; Vitoria, JoséIn the present work it is proved that the zeros of a unilateral octo- nionic polynomial belong to the conjugacy classes of the latent roots of an appropriate lambda-matrix. This allows the use of matricial norms, and matrix norms in particular, to obtain upper and lower bounds for the zeros of unilateral octonionic polynomials. Some results valid for complex and/or matrix polynomials are extended to octonionic polyno- mials.
- Eigenvalues of matrices related to the octonionsPublication . Serôdio, Rogério; Beites, P. D.; Vitoria, JoseA pseudo real matrix representation of an octonion, which is based on two real matrix represen- tations of a quaternion, is considered. We study how some operations defined on the octonions change the set of eigenvalues of the matrix obtained if these operations are performed after or before the matrix representation. The established results could be of particular interest to researchers working on estimation algorithms involving such operations.