Classical Geometries in Modern Contexts - Geometry of Real Inner Product Spaces
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Lieferung aus: Schweiz, Sofort per Download lieferbar.
Geometry of Real Inner Product Spaces, The basic structure playing the key role in this book is a real inner product space (X,?), i. e. a real vector space X together with a mapping ? : X× X ?R,a so-called inner product, satisfying rules (i), (ii), (iii), (iv) of section 1 of chapter 1. In order to avoid uninteresting cases from the point of view of geometry, we will assume throughout the whole book that there exist elements a,b in X which are linearly independent. But, on the other hand, we do not ask for the ex- tence of a positive integer n such that every subset S of X containing exactly n elementsislinearlydependent. Inotherwords,wedonotassumethatX isa?ni- dimensional vector space. So, when dealing in this book with di?erent geometries like euclidean, hyperbolic, elliptic, spherical, Lorentz-Minkowskian geometry or M¿ obius (Lie) sphere geometry over a real inner product space (X,?), the reader 2 3 mightthinkofX =R orR,ofX "nite-dimensional,orofX in?nite-dimensional. In fact, it plays no role, whatsoever, in our considerations whether the dimension ofX is "nite or in?nite: the theory as presenteddoes not depend onthe dimension of X. In this sense we maysaythat our presentationin question isdimension-free. The prerequisites for a fruitful reading of this book are essentially based on the sophomore level, especially after mastering basic linear algebra and basic 2 3 geometry ofR andR . Of course, hyperspheres are de?ned via the inner pr- uct ?. PDF, 19.01.2006.

Lieferung aus: Deutschland, Sofort per Download lieferbar.
Geometry of Real Inner Product Spaces The basic structure playing the key role in this book is a real inner product space (X,?), i. e. a real vector space X together with a mapping ? : X× X ?R,a so-called inner product, satisfying rules (i), (ii), (iii), (iv) of section 1 of chapter 1. In order to avoid uninteresting cases from the point of view of geometry, we will assume throughout the whole book that there exist elements a,b in X which are linearly independent. But, on the other hand, we do not ask for the ex- tence of a positive integer n such that every subset S of X containing exactly n elementsislinearlydependent. Inotherwords,wedonotassumethatX isa?ni- dimensional vector space. So, when dealing in this book with di?erent geometries like euclidean, hyperbolic, elliptic, spherical, Lorentz-Minkowskian geometry or M¿ obius (Lie) sphere geometry over a real inner product space (X,?), the reader 2 3 mightthinkofX =R orR,ofX "nite-dimensional,orofX in?nite-dimensional. In fact, it plays no role, whatsoever, in our considerations whether the dimension ofX is "nite or in?nite: the theory as presenteddoes not depend onthe dimension of X. In this sense we maysaythat our presentationin question isdimension-free. The prerequisites for a fruitful reading of this book are essentially based on the sophomore level, especially after mastering basic linear algebra and basic 2 3 geometry ofR andR . Of course, hyperspheres are de?ned via the inner pr- uct ?. 19.01.2006, PDF.

Lieferung aus: Deutschland, Sofort per Download lieferbar.
Geometry of Real Inner Product Spaces The basic structure playing the key role in this book is a real inner product space (X,?), i. e. a real vector space X together with a mapping ? : X× X ?R,a so-called inner product, satisfying rules (i), (ii), (iii), (iv) of section 1 of chapter 1. In order to avoid uninteresting cases from the point of view of geometry, we will assume throughout the whole book that there exist elements a,b in X which are linearly independent. But, on the other hand, we do not ask for the ex- tence of a positive integer n such that every subset S of X containing exactly n elementsislinearlydependent. Inotherwords,wedonotassumethatX isa?ni- dimensional vector space. So, when dealing in this book with di?erent geometries like euclidean, hyperbolic, elliptic, spherical, Lorentz-Minkowskian geometry or M¿ obius (Lie) sphere geometry over a real inner product space (X,?), the reader 2 3 mightthinkofX =R orR,ofX "nite-dimensional,orofX in?nite-dimensional. In fact, it plays no role, whatsoever, in our considerations whether the dimension ofX is "nite or in?nite: the theory as presenteddoes not depend onthe dimension of X. In this sense we maysaythat our presentationin question isdimension-free. The prerequisites for a fruitful reading of this book are essentially based on the sophomore level, especially after mastering basic linear algebra and basic 2 3 geometry ofR andR . Of course, hyperspheres are de?ned via the inner pr- uct ?. 19.01.2006, PDF.

Lieferung aus: Deutschland, Versandkostenfrei.
Classical Geometries in Modern Contexts: The basic structure playing the key role in this book is a real inner product space (X, ), i. e. a real vector space X together with a mapping : X× X R,a so-called inner product, satisfying rules (i), (ii), (iii), (iv) of section 1 of chapter 1. In order to avoid uninteresting cases from the point of view of geometry, we will assume throughout the whole book that there exist elements a,b in X which are linearly independent. But, on the other hand, we do not ask for the ex- tence of a positive integer n such that every subset S of X containing exactly n elementsislinearlydependent. Inotherwords,wedonotassumethatX isa ni- dimensional vector space. So, when dealing in this book with di erent geometries like euclidean, hyperbolic, elliptic, spherical, Lorentz-Minkowskian geometry or M¿ obius (Lie) sphere geometry over a real inner product space (X, ), the reader 2 3 mightthinkofX =R orR,ofX nite-dimensional,orofX in nite-dimensional. In fact, it plays no role, whatsoever, in our considerations whether the dimension ofX is nite or in nite: the theory as presenteddoes not depend onthe dimension of X. In this sense we maysaythat our presentationin question isdimension-free. The prerequisites for a fruitful reading of this book are essentially based on the sophomore level, especially after mastering basic linear algebra and basic 2 3 geometry ofR andR . Of course, hyperspheres are de ned via the inner pr- uct . Englisch, Ebook.

Lieferung aus: Japan, Lagernd, zzgl. Versandkosten.
This book is based on real inner product spaces X of arbitrary (finite or infinite) dimension greater than or equal to 2. With natural properties of (general) translations and general distances of X, euclidean and hyperbolic geometries are characterized. For these spaces X also the sphere geometries of Möbius and Lie are studied (besides euclidean and hyperbolic geometry), as well as geometries where Lorentz transformations play the key role. The geometrical notions of this book are based on general spaces X as described. This implies that also mathematicians who have not so far been especially interested in geometry may study and understand great ideas of classical geometries in modern and general contexts. Proofs of newer theorems, characterizing isometries and Lorentz transformations under mild hypotheses are included, like for instance infinite dimensional versions of famous theorems of A.D. Alexandrov on Lorentz transformations. A real benefit is the dimension-free approach to important geometrical theories. Only prerequisites are basic linear algebra and basic 2- and 3-dimensional real geometry. eBook.

Lieferung aus: Vereinigtes Königreich Großbritannien und Nordirland, Versandkostenfrei.
Classical Geometries in Modern Contexts ab 80.99 € als pdf eBook: Geometry of Real Inner Product Spaces. Aus dem Bereich: eBooks, Fachthemen & Wissenschaft, Wissenschaften allgemein,.

Lieferung aus: Deutschland, Versandkostenfrei.
Classical Geometries in Modern Contexts: The basic structure playing the key role in this book is a real inner product space (X, ), i. e. a real vector space X together with a mapping : X? X R,a so-called inner product, satisfying rules (i), (ii), (iii), (iv) of section 1 of chapter 1. In order to avoid uninteresting cases from the point of view of geometry, we will assume throughout the whole book that there exist elements a,b in X which are linearly independent. But, on the other hand, we do not ask for the ex- tence of a positive integer n such that every subset S of X containing exactly n elementsislinearlydependent. Inotherwords,wedonotassumethatX isa ni- dimensional vector space. So, when dealing in this book with di erent geometries like euclidean, hyperbolic, elliptic, spherical, LorentzMinkowskian geometry or M obius (Lie) sphere geometry over a real inner product space (X, ), the reader 2 3 mightthinkofX =R orR,ofX nite-dimensional,orofX in nite-dimensional. In fact, it plays no role, whatsoever, in our considerations whether the dimension ofX is nite or in nite: the theory as presenteddoes not depend onthe dimension of X. In this sense we maysaythat our presentationin question isdimension-free. The prerequisites for a fruitful reading of this book are essentially based on the sophomore level, especially after mastering basic linear algebra and basic 2 3 geometry ofR andR . Of course, hyperspheres are de ned via the inner pr- uct . Englisch, Ebook.

Lieferung aus: Vereinigtes Königreich Großbritannien und Nordirland, Versandkostenfrei.
Classical Geometries in Modern Contexts ab 70.99 € als pdf eBook: Geometry of Real Inner Product Spaces. 2005. Auflage. Aus dem Bereich: eBooks, Fachthemen & Wissenschaft, Wissenschaften allgemein,.

Lieferung aus: Vereinigtes Königreich Großbritannien und Nordirland, Versandkostenfrei.
Classical Geometries in Modern Contexts ab 70.99 EURO Geometry of Real Inner Product Spaces. 2005. Auflage.

Lieferung aus: Schweiz, Sofort per Download lieferbar.
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