{"product_id":"9783032414762","title":"Linear Algebra II Foundations and Applications: Eigenvalues and Geometry","description":"\u003ch1\u003eLinear Algebra II\u003c\/h1\u003e\u003ch2\u003eFoundations and Applications: Eigenvalues and Geometry\u003c\/h2\u003e\u003ch3\u003ePeter Knabner | Wolf Barth\u003c\/h3\u003e\u003cdiv\u003e\u003cb\u003eMathematics \/ General\u003c\/b\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\n\u003cp\u003eThese volumes introduce and develop the theory of linear structures for students of mathematics and its applications. Today, linear algebra serves as an essential tool and unifying language across nearly all areas of mathematics. Given its importance in the natural sciences, engineering, and economics, linear algebra is presented as a valuable and widely applicable subject in its own right.\u003c\/p\u003e\n\u003cp\u003eIn addition to the standard core material, the volume includes topics of interest to students from a variety of disciplines. Students of mathematics education will find an introduction to several aspects of analytic geometry. In this second volume, the study of analytic geometry is extended through a treatment of quadrics and, in particular, the theory of polyhedra, culminating in linear optimization and the simplex algorithm. Readers with an interest in algebra are introduced to bi- and multilinear forms and multilinear algebra, while those interested in analysis or physics will find a thorough treatment of spectral theory and linear ordinary differential equations. The Schur and Jordan normal forms, including their real counterparts, are fundamental to the development of the theory.\u003c\/p\u003e\n\u003cp\u003eThroughout, structural insights are combined with practical algorithmic methods. The treatment of tensor calculus helps bridge the gap between the mathematical and engineering perspectives, while convex geometry facilitates the transition to functional analysis and its applications. Students pursuing numerical mathematics, optimization, or data-oriented applications will encounter topics such as singular value decomposition, principal component analysis, and linear and quadratic optimization. Numerical methods are further developed through the study of least-squares problems and QR decomposition, providing a foundation for the modern eigenvalue algorithms described in Volume 3. Many of these topics are also of special relevance to students of economics and related disciplines.\u003c\/p\u003e\n\u003cp\u003eParticular emphasis is placed on connecting theory and algorithms and on relating both to applications in the sciences. To support this goal, mathematical modelling plays a central role. Ongoing examples drawn from mechanics, electrical networks, and economics are developed progressively alongside the theory. \u003c\/p\u003e\n\u003c\/div\u003e\u003cdiv\u003e\n\u003cp\u003ePeter Knabner is a German mathematician and currently Professor Emeritus of Applied Mathematics at the University Erlangen-Nuremberg after over 20 years in office as chaired professor. In his research he developed and analyzed mathematical models and their numerical schemes for multiphase flow and reactive multicomponent transport in porous media. He is the author of well over 160 peer-reviewed publications in applied analysis, numerical mathematics, and hydrogeology, as well as author and co-author of 14 monographs and textbooks in English and German, including those on the numerical methods for partial differential equations, mathematical modeling, and linear algebra.\u003c\/p\u003e\n\u003cp\u003eWolf Barth was a German mathematician and has been in office as a chaired professor at the University Erlangen-Nuremberg for over 30 years. In his research, he investigated vector bundles and projective surfaces (Barth surface). He had a strong dedication to teaching, in particular linear algebra.\u003c\/p\u003e\n\u003c\/div\u003e\u003cbr\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublication Date: \u003c\/td\u003e\n\u003ctd\u003e25 August 2027\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublisher: \u003c\/td\u003e\n\u003ctd\u003eSpringer Nature Switzerland\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eImprint: \u003c\/td\u003e\n\u003ctd\u003eSpringer\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eISBN-13: \u003c\/td\u003e\n\u003ctd\u003e9783032414762\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eFormat: \u003c\/td\u003e\n\u003ctd\u003eHardback\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e","brand":"Springer Nature Switzerland","offers":[{"title":"Default Title","offer_id":57339783446668,"sku":"9783032414762","price":71.99,"currency_code":"USD","in_stock":true}],"url":"https:\/\/lateknightbooks.com\/products\/9783032414762","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}