D'Alembert's proof of the fundamental theorem of algebra
نویسندگان
چکیده
منابع مشابه
A linear algebra proof of the fundamental theorem of algebra
We present a recent proof due to Harm Derksen, that any linear operator in a complex finite dimensional vector space admits eigenvectors. The argument avoids the use of the fundamental theorem of algebra, which can then be deduced from it. Our presentation avoids any appeal to the theory of determinants. 2010 Mathematics Subject Classification. 15-01, 15A18.
متن کاملA Probabilistic Proof of the Fundamental Theorem of Algebra
We use Lévy’s theorem on invariance of planar Brownian motion under conformal maps and the support theorem for Brownian motion to show that the range of a non-constant polynomial of a complex variable consists of the whole complex plane. In particular, we obtain a probabilistic proof of the fundamental theorem of algebra.
متن کاملAn Elementary Proof of the Fundamental Theorem of Tropical Algebra
In this paper we give an elementary proof of the Fundamental Theorem of Algebra for polynomials over the rational tropical semi-ring. We prove that, tropically, the rational numbers are algebraically closed. We provide a simple algorithm for factoring tropical polynomials of a single variable. A central idea is the concept of least-coefficient polynomials as representatives for classes of funct...
متن کاملAnother Proof of the Fundamental Theorem of Algebra
Theorem 1 (Fundamental Theorem of Algebra). Every non-constant polynomial with complex coefficients has a root in C. This is the strategy of the proof. Let Xn ' C be the space of degree n monic polynomials with complex coefficients, via the identification (a1, ..., an) 7→ z + ∑n i=1 aiz . Let D ⊂ Xn be the zero locus of the discriminant, and let R ⊂ Xn \ D be the set of polynomials with non-zer...
متن کاملThe Fundamental Theorem of Algebra: an Elementary and Direct Proof
We present a simple, differentiation-free, integrationfree, trigonometryfree, direct and elementary proof of the Fundamental Theorem of Algebra. “The final publication (in The Mathematical Intelligencer, 33, No. 2 (2011), 1-2) is available at www.springerlink.com: http://www.springerlink.com/content/l1847265q2311325/”
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Historia Mathematica
سال: 2004
ISSN: 0315-0860
DOI: 10.1016/j.hm.2003.12.001