Related papers: A Proof of The Fundamental Theorem of Algebra
There are several proofs of the Fundamental Theorem of Algebra, mainly using algebra, analysis and topology. In this article, we have shown that the Fundamental Theorem of Algebra can be proved using Nevanlinna's first fundamental theorem…
Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.
We present a simple short proof of the Fundamental Theorem of Algebra, without complex analysis and with a minimal use of topology. It can be taught in a first year calculus class.
We give a new proof of the fundamental theorem of algebra. It is entirely elementary, focused on using long division to its fullest extent. Further, the method quickly recovers a more general version of the theorem recently obtained by…
D'Alembert made the first serious attempt to prove the Fundamental Theorem of Algebra (FTA) in 1746. An elementary proof of (FTA) based on the same idea is given in Proofs from THE BOOK. We give a shorter and more transperant version of…
Proofs of the fundamental theorem of algebra can be divided up into three groups according to the techniques involved: proofs that rely on real or complex analysis, algebraic proofs, and topological proofs. Algebraic proofs make use of the…
Two well known facts from elementary number theory are proven by using Bergman spaces.
In this paper we show an index theorem for gerbes
We give an elementary proof of a Landesman-Lazer type result for systems by means of a shooting argument and explore its connection with the fundamental theorem of algebra.
This paper presents an elementary and direct proof of the Fundamental Theorem of Algebra, via Bolzano-Weierstrass Theorem on Minima, that avoids: every root extraction, angle, non-algebraic functions, differentiation, integration, series…
We present an elementary proof of the fundamental theorem of algebra, following Cauchy's version but avoiding his use of circular functions. It is written in the same spirit as Littlewood's proof of 1941, but reduces it to more elementary…
In this paper motivated by the celebrated fundamental theorem of algebra and its standard proof utilizing Liouville's Theorem, we prove the fundamental theorem of algebra type results for both commutative and noncommutative polynomials in…
This paper shows an elementary and direct proof of the Fundamental Theorem of Algebra, via Bolzano-Weierstrass Theorem on Minima and the Binomial Formula, that avoids: any root extraction other than the one used to define the modulus…
This paper presents an alternative proof of the Fundamental Theorem of Algebra that has several distinct advantages. The proof is based on simple ideas involving continuity and differentiation. Visual software demonstrations can be used to…
A weak version of Birkhoff's generalization of the Perron-Frobenius theorem states that every endomorphism of a finite-dimensional real vector that leaves invariant a non-degenerate closed convex cone has an eigenvector in that cone. Here,…
In this short paper we review and extract some features of the Fredholm Alternative problem .
A simple but rigorous proof of the Fundamental Theorem of Calculus is given in geometric calculus, after the basis for this theory in geometric algebra has been explained. Various classical examples of this theorem, such as the Green's and…
We establish an analogue of the fundamental theorem of algebra for polynomial matrix equations, in which the matrices-coefficients and unknown matrix are assumed to be circulant matrices.
The main aim of the present paper is to represent an exact and simple proof for FLT by using properties of the algebra identities and linear algebra.
Many proofs of the fundamental theorem of algebra rely on the fact that the minimum of the modulus of a complex polynomial over the complex plane is attained at some complex number. The proof then follows by arguing the minimum value is…