Zobrazeno 1 - 10 of 16 pro vyhledávání: '"Alexey O. Remizov"'
1
Elektronická kniha
Linear Algebra and Geometry
Autor: Igor R. Shafarevich, Alexey O. Remizov
This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continu
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4
Quadratic and Bilinear Forms
Autor: Alexey O. Remizov, Igor R. Shafarevich
Publikováno v: Linear Algebra and Geometry ISBN: 9783642309939
Quadratic and bilinear forms on vector spaces are considered. A connection between the notion of bilinear form and that of linear transformation is established, based on the isomorphism between the space of bilinear forms and the space of linear tran
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::b39d6f3c230deb115c8ee745257caefd
https://doi.org/10.1007/978-3-642-30994-6_6
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5
Groups, Rings, and Modules
Autor: Igor R. Shafarevich, Alexey O. Remizov
Publikováno v: Linear Algebra and Geometry ISBN: 9783642309939
This chapter presents an excursion in abstract algebra. It begins with the notions of group, subgroup, direct sum, homomorphism, isomorphism, etc., their basic properties, and numerous examples. This is justified by the main aim of the chapter: to es
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::ed2da240b021efab1a091d2d72fb7f67
https://doi.org/10.1007/978-3-642-30994-6_13
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7
Matrices and Determinants
Autor: Alexey O. Remizov, Igor R. Shafarevich
Publikováno v: Linear Algebra and Geometry ISBN: 9783642309939
In the second chapter we deal with matrices and determinants. The chapter starts with determinants of second and third orders, which are defined through solutions of linear algebraic systems; determinants of arbitrary order are defined inductively. T
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::05b4320f363ce5a2cde58ccc508bc35c
https://doi.org/10.1007/978-3-642-30994-6_2
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8
The Exterior Product and Exterior Algebras
Autor: Alexey O. Remizov, Igor R. Shafarevich
Publikováno v: Linear Algebra and Geometry ISBN: 9783642309939
The chapter begins with notion of the Plucker coordinates of a subspace in a vector space. Then the Plucker relations are derived, and the Grassmann varieties are described. Then an exterior product of vectors is defined, and the connection between t
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::79a746d09f808b578b8ee7d27d113be4
https://doi.org/10.1007/978-3-642-30994-6_10
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10
Elements of Representation Theory
Autor: Igor R. Shafarevich, Alexey O. Remizov
Publikováno v: Linear Algebra and Geometry ISBN: 9783642309939
The final chapter of the book presents the basic elements of representation theory, especially finite-dimensional representations of finite groups. For instance, it is proved that every representation of a finite group is a direct sum of irreducible
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::8908282a24f797007ed14a0ed6488f55
https://doi.org/10.1007/978-3-642-30994-6_14
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