Linear Algebra and Geometry

A Second Course

Author: Irving Kaplansky

Publisher: Courier Corporation

ISBN: 9780486432335

Category: Mathematics

Page: 143

View: 1929

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The author of this text seeks to remedy a common failing in teaching algebra: the neglect of related instruction in geometry. Focusing on inner product spaces, orthogonal similarity, and elements of geometry, this volume is illustrated with an abundance of examples, exercises, and proofs and is suitable for both undergraduate and graduate courses. 1974 edition.
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Linear Geometry

Author: Rafael Artzy

Publisher: N.A

ISBN: 9780486466279

Category: Mathematics

Page: 273

View: 2686

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Most linear algebra texts neglect geometry in general and linear geometry in particular. This text for advanced undergraduates and graduate students stresses the relationship between algebra and linear geometry. It begins by using the complex number plane as an introduction to a variety of transformations and their groups in the Euclidean plane, explaining algebraic concepts as they arise. A brief account of Poincaré's model of the hyperbolic plane and its transformation group follow. Succeeding chapters contain a systematic treatment of affine, Euclidean, and projective spaces over fields that emphasizes transformations and their groups, along with an outline of results involving other geometries. An examination of the foundations of geometry starts from rudimentary projective incidence planes, then gradually adjoins axioms and develops various non-Desarguesian, Desarguesian, and Pappian planes, their corresponding algebraic structures, and their collineation groups. The axioms of order, continuity, and congruence make their appearance and lead to Euclidean and non-Euclidean planes. Lists of books for suggested further reading follow the third and fourth chapters, and the Appendix provides lists of notations, axioms, and transformation groups.
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Lectures on Linear Algebra

Author: I. M. Gelfand

Publisher: Courier Corporation

ISBN: 9780486660820

Category: Mathematics

Page: 185

View: 1298

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Prominent Russian mathematician's concise, well-written exposition considers n-dimensional spaces, linear and bilinear forms, linear transformations, canonical form of an arbitrary linear transformation, and an introduction to tensors. While not designed as an introductory text, the book's well-chosen topics, brevity of presentation, and the author's reputation will recommend it to all students, teachers, and mathematicians working in this sector.
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Linear Algebra and Projective Geometry

Author: Reinhold Baer

Publisher: Courier Corporation

ISBN: 0486154661

Category: Mathematics

Page: 336

View: 6642

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Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. 1952 edition.
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Geometry of Complex Numbers

Author: Hans Schwerdtfeger

Publisher: Courier Corporation

ISBN: 0486135861

Category: Mathematics

Page: 224

View: 5991

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Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.
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Matrices and Linear Algebra

Author: Hans Schneider,George Phillip Barker

Publisher: Courier Corporation

ISBN: 0486139301

Category: Mathematics

Page: 432

View: 2822

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Basic textbook covers theory of matrices and its applications to systems of linear equations and related topics such as determinants, eigenvalues, and differential equations. Includes numerous exercises.
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Nonnegative Matrices and Applicable Topics in Linear Algebra

Author: Alexander Graham

Publisher: Dover Publications

ISBN: 0486838072

Category: Mathematics

Page: 272

View: 8874

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Nonnegative matrices is an increasingly important subject in economics, control theory, numerical analysis, Markov chains, and other areas. This concise treatment is directed toward undergraduates who lack specialized knowledge at the postgraduate level of mathematics and related fields, such as mathematical economics and operations research. An Introductory Survey encompasses some aspects of matrix theory and its applications and other relevant topics in linear algebra, including certain facets of graph theory. Subsequent chapters cover various points of the theory of normal matrices, comprising unitary and Hermitian matrices, and the properties of positive definite matrices. An exploration of the main topic, nonnegative matrices, is followed by a discussion of M-matrices. The final chapter examines stochastic, genetic, and economic models. The important concepts are illustrated by simple worked examples. Problems appear at the conclusion of most chapters, with solutions at the end of the book.
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An Introduction to Linear Algebra

Author: L. Mirsky

Publisher: Courier Corporation

ISBN: 0486166449

Category: Mathematics

Page: 464

View: 5414

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Rigorous, self-contained coverage of determinants, vectors, matrices and linear equations, quadratic forms, more. Elementary, easily readable account with numerous examples and problems at the end of each chapter.
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A Vector Space Approach to Geometry

Author: Melvin Hausner

Publisher: Courier Dover Publications

ISBN: 0486835391

Category: Mathematics

Page: 416

View: 7568

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A fascinating exploration of the correlation between geometry and linear algebra, this text portrays the former as a subject better understood by the use and development of the latter rather than as an independent field. The treatment offers elementary explanations of the role of geometry in other branches of math and science — including physics, analysis, and group theory — as well as its value in understanding probability, determinant theory, and function spaces. Outstanding features of this volume include discussions of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. Students and other mathematically inclined readers will find that this inquiry into the interplay between geometry and other areas offers an enriched appreciation of both subjects.
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Linear Algebra

Author: Sterling K. Berberian

Publisher: Courier Corporation

ISBN: 0486780554

Category: Mathematics

Page: 358

View: 9238

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Introductory treatment covers basic theory of vector spaces and linear maps — dimension, determinants, eigenvalues, and eigenvectors — plus more advanced topics such as the study of canonical forms for matrices. 1992 edition.
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