Polynomials and degrees of maps in real normed algebras
Let 𝒜 be the algebra of quaternions ℍ or octonions 𝕆. In this manuscript an elementary proof is given, based on ideas of Cauchy and D’Alembert, of the fact that an ordinary polynomial f(t) ∈ 𝒜[t] has a root in 𝒜. As a consequence, the Jacobian determinant |J(f)| is always nonnegative in 𝒜. Moreover,...
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| Format: | Article |
| Language: | English |
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Sciendo
2020-06-01
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| Series: | Communications in Mathematics |
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| Online Access: | https://doi.org/10.2478/cm-2020-0004 |