Linear Algebra and Geometry

Buch | Hardcover
XXII, 526 Seiten
2012 | 2013
Springer Berlin (Verlag)
978-3-642-30993-9 (ISBN)
69,54 inkl. MwSt
Opening with the theory of linear algebraic equations and basic elements of matrix theory, this book includes topics not usually covered: exterior algebras, non-Euclidean geometry, theory of quadrics and more. Offers examples from various mathematical fields.
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 continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics.

Preface.- Preliminaries.- 1. Linear Equations.- 2. Matrices and Determinants.- 3. Vector Spaces.- 4. Linear Transformations of a Vector Space to Itself.- 5. Jordan Normal Form.- 6. Quadratic and Bilinear Forms.- 7. Euclidean Spaces.- 8. Affine Spaces.- 9. Projective Spaces.- 10. The Exterior Product and Exterior Algebras.- 11. Quadrics.- 12. Hyperbolic Geometry.- 13. Groups, Rings, and Modules.- 14. Elements of Representation Theory.- Historical Note.- References.- Index

lt;p>From the reviews:

"Shafarevich (Russian Academy of Sciences) and Remizov (École Polytechnique, CNRS, France) provide insightful comments that apply not only to linear algebra but also to mathematics in general. ... The book is quite readable ... . Summing Up: Recommended. Upper-division undergraduates, graduate students, researchers/faculty, and professionals." (J. R. Burke, Choice, Vol. 50 (8), April, 2013)

"This beautiful textbook not only reflects I. R. Shafarevich's unrivalled mastery of mathematical teaching and expository writing, but also the didactic principles of the Russian mathematical school in teaching basic courses such as linear algebra and analytic geometry. ... made accessible to a wide audience of international readers, and to further generations of students, too. ... this book may be regarded as a historical document in the relevant textbook literature ... ." (Werner Kleinert, Zentralblatt MATH, Vol. 1256, 2013)

Erscheint lt. Verlag 24.8.2012
Übersetzer David P Kramer, Lena Nekludova
Zusatzinfo XXII, 526 p.
Verlagsort Berlin
Sprache englisch
Maße 155 x 235 mm
Gewicht 958 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Geometrie / Topologie
Schlagworte groups, rings, modules • linear algerba • Lineare Algebra • Matrix • matrix theory • projective space • Vector Space
ISBN-10 3-642-30993-3 / 3642309933
ISBN-13 978-3-642-30993-9 / 9783642309939
Zustand Neuware
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