Frobenius' Theorem states that, besides the fields of real and complex numbers, the algebra of quaternions H is the only finite-dimensional real division algebra. We first give a short elementary proof of this theorem, then characterize finite-dimensional real algebras that contain either a copy ...
Lagrange’s theorem on finite groups Sturm’s theorem Galois theory See all related content group theory, inmodern algebra, the study of groups, which are systems consisting of a set of elements and abinaryoperation that can be applied to two elements of the set, which together satisfy certain...
1.This paper introduces an important Perron-Frobenius theorem in algebra,and discusses the first principal component served as the principle and condition of the system evaluation index.介绍了代数学中的一个重要定理(Perron-Frobenius定理),论述了第一主成分作为系统评估指数的原理和条件;对两类系统排序评估...
On the Fundamental Theorem of Algebra and Its Equivalence to the Frobenius Theorem on Division Algebras In this article we give a new proof of the Fundamental Theorem of Algebra. Our proof is algebraic. We simplify the known proof of the Fundamental Theorem c... IS Jabbarov,GK Hasanova - ...
Denote by M n (C) (respectively, M n (R)) the algebra of complex(respectively, real) n × n matrices. Given A ∈ M n (C), the spectrum of A is denotedby σ (A), and the spectral radius of A is denoted by ρ(A).∗† Division of Engineering and Mathematics, University ...
2) Perron-Frobenius theorem Perron-Frobenius定理 1. This paper introduces an important Perron-Frobenius theorem in algebra,and discusses the first principal component served as the principle and condition of the system evaluation index. 介绍了代数学中的一个重要定理(Perron-Frobenius定理),论述了第一...
2) Perron-Frobenius theorem Perron-Frobenius定理 1. This paper introduces an important Perron-Frobenius theorem in algebra,and discusses the first principal component served as the principle and condition of the system evaluation index. 介绍了代数学中的一个重要定理(Perron-Frobenius定理),论述了第一...
Mazur''s theorem [19] states that every normed division algebra over the field of real numbers is isomorphic to either the field R of real numbers, the field C of complex numbers, or the non-commutative algebra Q of quaternions. Gelfand [15] proved that every normed division algebra over ...
In this article we give a new proof of the Fundamental Theorem of Algebra. Our proof is algebraic. We simplify the known proof of the Fundamental Theorem considering special case of polynomials of odd degree with real coefficients. This case allows us to apply the method of mathematical ...
Furthermore, we establish some algebraic properties for hypermatrices and then proceed to extend the Perron-Frobenius Theorem for this setting and prove the existence of a unique eigenvalue. We continue by stating a result from Nussbaum, that the Min-Max theorem holds, and provide a proof for ...