Matrix versions of Real and Quaternionic Nullstellensätze
نویسندگان
چکیده
Real Nullstellensatz is a classical result from Algebraic Geometry. It has recently been extended to quaternionic polynomials by Alon and Paran [1]. The aim of this paper extend their Quaternionic matrix polynomials. We also obtain an improvement the for [4] in sense that we simplify definition real left ideal. use methods proof version Hilbert's [5] extensions mildly non-commutative case case.
منابع مشابه
Comparison of congruences and strict equivalences for real, complex, and quaternionic matrix pencils with symmetries
The equivalence relations of strict equivalence and congruence of real and complex matrix pencils with symmetries are compared, depending on whether the congruence matrices are real, complex, or quaternionic. The obtained results are applied to comparison of congruences of matrices, over the reals, the complexes, and the quaternions.
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The equivalence relations of strict equivalence and congruence of real and complex matrix pencils with symmetries are compared, depending on whether the congruence matrices are real, complex, or quaternionic. The obtained results are applied to comparison of congruences of matrices, over the reals, the complexes, and the quaternions.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2022
ISSN: ['1090-266X', '0021-8693']
DOI: https://doi.org/10.1016/j.jalgebra.2022.06.038