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Serge Lang (French:; May 19, 1927 – September 12, 2005) was a French-American mathematician and activist who taught at Yale University for most of his career. He is known for his work in number theory and for his mathematics textbooks, including the influential Algebra .
Despite a bad press initially, Lang's conception has been sufficiently widely accepted for a 2006 tribute to call the book "visionary". [5] A larger field sometimes called arithmetic of abelian varieties now includes Diophantine geometry along with class field theory, complex multiplication, local zeta-functions and L-functions. [6] Paul Vojta ...
Concerning general linear maps, linear endomorphisms, and square matrices have some specific properties that make their study an important part of linear algebra, which is used in many parts of mathematics, including geometric transformations, coordinate changes, quadratic forms, and many other parts of mathematics.
Introduction to Linear Algebra, Fifth Edition (2016) [21] [22] Differential Equations and Linear Algebra (2014) Differential Equations and Linear Algebra - New Book Website; Essays in Linear Algebra (2012) Algorithms for Global Positioning, with Kai Borre (2012) An Analysis of the Finite Element Method, with George Fix (2008) Computational ...
Steinberg () gave a useful improvement to the theorem.. Suppose that F is an endomorphism of an algebraic group G.The Lang map is the map from G to G taking g to g −1 F(g).. The Lang–Steinberg theorem states [3] that if F is surjective and has a finite number of fixed points, and G is a connected affine algebraic group over an algebraically closed field, then the Lang map is surjective.
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication.
Template: Lang Algebra. 11 languages. ... Download as PDF; Printable version; In other projects ...
For instance, a "map" is a "continuous function" in topology, a "linear transformation" in linear algebra, etc. Some authors, such as Serge Lang, [8] use "function" only to refer to maps in which the codomain is a set of numbers (i.e. a subset of R or C), and reserve the term mapping for more general functions.
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