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An extension of a work of Hellmuth Kneser on the Fundamental Theorem of Algebra). Ostrowski, Alexander (1920), "Über den ersten und vierten Gaußschen Beweis des Fundamental-Satzes der Algebra", Carl Friedrich Gauss Werke Band X Abt. 2 (tr. On the first and fourth Gaussian proofs of the Fundamental Theorem of Algebra).
Inverse eigenvalues theorem (linear algebra) Perron–Frobenius theorem (matrix theory) Principal axis theorem (linear algebra) Rank–nullity theorem (linear algebra) Rouché–Capelli theorem (Linear algebra) Sinkhorn's theorem (matrix theory) Specht's theorem (matrix theory) Spectral theorem (linear algebra, functional analysis)
In 1806 Jean-Robert Argand independently issued a pamphlet on complex numbers and provided a rigorous proof of the fundamental theorem of algebra. [35] Carl Friedrich Gauss had earlier published an essentially topological proof of the theorem in 1797 but expressed his doubts at the time about "the true metaphysics of the square root of −1". [36]
The first proof of the fundamental theorem of algebra in 1799 contained an essentially topological argument; fifty years later, he further developed the topological argument in his fourth proof of this theorem. [209] Gauss bust by Heinrich Hesemann (1855) [x]
Fermat's little theorem and some proofs; Gödel's completeness theorem and its original proof; Mathematical induction and a proof; Proof that 0.999... equals 1; Proof that 22/7 exceeds π; Proof that e is irrational; Proof that π is irrational; Proof that the sum of the reciprocals of the primes diverges
In mathematics, a fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus . [ 1 ]
As the common roots of two polynomials are the roots of their greatest common divisor, Bézout's identity and fundamental theorem of algebra imply the following result: For univariate polynomials f and g with coefficients in a field, there exist polynomials a and b such that af + bg = 1 if and only if f and g have no common root in any ...
The fundamental theorem of algebra; Monsky's theorem (4th edition) Van der Waerden's conjecture; Littlewood–Offord lemma; Buffon's needle problem; Sperner's theorem, Erdős–Ko–Rado theorem and Hall's theorem; Lindström–Gessel–Viennot lemma and the Cauchy–Binet formula; Four proofs of Cayley's formula; Kakeya sets in vector spaces ...