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Linear Algebra Geometry and Transformation

Linear Algebra  Geometry and Transformation Author Bruce Solomon
ISBN-10 9781482299304
Release 2014-12-12
Pages 474
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The Essentials of a First Linear Algebra Course and More Linear Algebra, Geometry and Transformation provides students with a solid geometric grasp of linear transformations. It stresses the linear case of the inverse function and rank theorems and gives a careful geometric treatment of the spectral theorem. An Engaging Treatment of the Interplay among Algebra, Geometry, and Mappings The text starts with basic questions about images and pre-images of mappings, injectivity, surjectivity, and distortion. In the process of answering these questions in the linear setting, the book covers all the standard topics for a first course on linear algebra, including linear systems, vector geometry, matrix algebra, subspaces, independence, dimension, orthogonality, eigenvectors, and diagonalization. A Smooth Transition to the Conceptual Realm of Higher Mathematics This book guides students on a journey from computational mathematics to conceptual reasoning. It takes them from simple "identity verification" proofs to constructive and contrapositive arguments. It will prepare them for future studies in algebra, multivariable calculus, and the fields that use them.



Linear Algebra and Projective Geometry

Linear Algebra and Projective Geometry Author Reinhold Baer
ISBN-10 9780486154664
Release 2012-06-11
Pages 336
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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.



Matrices and Transformations

Matrices and Transformations Author Anthony J. Pettofrezzo
ISBN-10 9780486151809
Release 2012-05-04
Pages 144
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Elementary, concrete approach: fundamentals of matrix algebra, linear transformation of the plane, application of properties of eigenvalues and eigenvectors to study of conics. Includes proofs of most theorems. Answers to odd-numbered exercises.



Linear Algebra and Geometry

Linear Algebra and Geometry Author Igor R. Shafarevich
ISBN-10 9783642309946
Release 2012-08-23
Pages 526
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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.



Linear Algebra Through Geometry

Linear Algebra Through Geometry Author Thomas Banchoff
ISBN-10 9781461243908
Release 2012-12-06
Pages 308
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This book introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations, and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues, and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other finite-dimensional vector space.



Matrices and Linear Algebra

Matrices and Linear Algebra Author Hans Schneider
ISBN-10 9780486139302
Release 2012-06-08
Pages 432
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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.



Matrices and Linear Transformations

Matrices and Linear Transformations Author Charles G. Cullen
ISBN-10 9780486132419
Release 2012-09-20
Pages 336
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Undergraduate-level introduction to linear algebra and matrix theory. Explores matrices and linear systems, vector spaces, determinants, spectral decomposition, Jordan canonical form, much more. Over 375 problems. Selected answers. 1972 edition.



Lectures on Linear Algebra

Lectures on Linear Algebra Author I. M. Gelfand
ISBN-10 0486660826
Release 1989
Pages 185
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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.



Linear Algebra

Linear Algebra Author E. Sernesi
ISBN-10 0412406802
Release 1993-05-15
Pages 384
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This is an undergraduate textbook suitable for linear algebra courses. This is the only textbook that develops the linear algebra hand-in-hand with the geometry of linear (or affine) spaces in such a way that the understanding of each reinforces the other. The text is divided into two parts: Part I is on linear algebra and affine geometry, finishing with a chapter on transformation groups; Part II is on quadratic forms and their geometry (Euclidean geometry), including a chapter on finite subgroups of 0 (2). Each of the 23 chapters concludes with a generous helping of exercises, and a selection of these have solutions at the end of the book. The chapters also contain many examples, both numerical worked examples (mostly in 2 and 3 dimensions), as well as examples which take some of the ideas further. Many of the chapters contain "complements" which develop more special topics, and which can be omitted on a first reading. The structure of the book is designed to allow as much flexibility as possible in designing a course, either by omitting whole chapters or by omitting the "complements" or specific examples.



Geometric Linear Algebra

Geometric Linear Algebra Author I-Hsiung Lin
ISBN-10 9789812707758
Release 2008
Pages 806
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This accessible book for beginners uses intuitive geometric concepts to create abstract algebraic theory with a special emphasis on geometric characterizations. The book applies known results to describe various geometries and their invariants, and presents problems concerned with linear algebra, such as in real and complex analysis, differential equations, differentiable manifolds, differential geometry, Markov chains and transformation groups. The clear and inductive approach makes this book unique among existing books on linear algebra both in presentation and in content.



Advanced Linear Algebra

Advanced Linear Algebra Author Bruce Cooperstein
ISBN-10 9781439829691
Release 2016-04-19
Pages 364
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Advanced Linear Algebra focuses on vector spaces and the maps between them that preserve their structure (linear transformations). It starts with familiar concepts and then slowly builds to deeper results. Along with including many exercises and examples, each section reviews what students need to know before studying the material. The book first introduces vector spaces over fields as well as the fundamental concepts of linear combinations, span of vectors, linear independence, basis, and dimension. After covering linear transformations, it discusses the algebra of polynomials with coefficients in a field, concentrating on results that are consequences of the division algorithm. The author then develops the whole structure theory of a linear operator on a finite dimensional vector space from a collection of some simple results. He also explores the entire range of topics associated with inner product spaces, from the Gram–Schmidt process to the spectral theorems for normal and self-adjoint operators on an inner product space. The text goes on to rigorously describe the trace and determinant of linear operators and square matrices. The final two chapters focus on bilinear forms and tensor products and related material. Designed for advanced undergraduate and beginning graduate students, this textbook shows students the beauty of linear algebra. It also prepares them for further study in mathematics.



Linear Algebra and Matrix Theory

Linear Algebra and Matrix Theory Author Robert R. Stoll
ISBN-10 9780486265216
Release 2013-05-20
Pages 288
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One of the best available works on matrix theory in the context of modern algebra, this text bridges the gap between ordinary undergraduate studies and completely abstract mathematics. 1952 edition.



A Vector Space Approach to Geometry

A Vector Space Approach to Geometry Author Melvin Hausner
ISBN-10 9780486137858
Release 2012-10-30
Pages 416
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This examination of geometry's correlation with other branches of math and science features a review of systematic geometric motivations in vector space theory and matrix theory; more. 1965 edition.



The Four Pillars of Geometry

The Four Pillars of Geometry Author John Stillwell
ISBN-10 9780387255309
Release 2005-08-09
Pages 228
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This book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariants Approach makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic Abundantly supplemented with figures and exercises



Vector Geometry

Vector Geometry Author Gilbert de B. Robinson
ISBN-10 9780486321042
Release 2013-10-10
Pages 192
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Concise undergraduate-level text by a prominent mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement. Includes answers to exercises. 1962 edition.



Linear Algebra

Linear Algebra Author Georgi? Evgen?evich Shilov
ISBN-10 048663518X
Release 1977
Pages 387
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Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.



Geometries and Transformations

Geometries and Transformations Author Norman W. Johnson
ISBN-10 9781107103405
Release 2018-04-30
Pages 350
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A readable exposition of how Euclidean and other geometries can be distinguished using linear algebra and transformation groups.