Linear Algebra

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9780486635187: Linear Algebra

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.

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chapter 1 DETERMINANTS 1.1. Number Fields 1.2. Problems of the Theory of Systems of Linear Equations 1.3. Determinants of Order n 1.4. Properties of Determinants 1.5. Cofactors and Minors 1.6. Practical Evaluation of Determinants 1.7. Cramer's Rule 1.8. Minors of Arbitrary Order. Laplace's Theorem 1.9. Linear Dependence between Columns Problems chapter 2 LINEAR SPACES 2.1. Definitions 2.2. Linear Dependence 2.3. "Bases, Components, Dimension" 2.4. Subspaces 2.5. Linear Manifolds 2.6. Hyperplanes 2.7. Morphisms of Linear Spaces Problems chapter 3 SYSTEMS OF LINEAR EQUATIONS 3.1. More on the Rank of a Matrix 3.2. Nontrivial Compatibility of a Homogeneous Linear System 3.3. The Compatability Condition for a General Linear System 3.4. The General Solution of a Linear System 3.5. Geometric Properties of the Solution Space 3.6. Methods for Calculating the Rank of a Matrix Problems chapter 4 LINEAR FUNCTIONS OF A VECTOR ARGUMENT 4.1. Linear Forms 4.2. Linear Operators 4.3. Sums and Products of Linear Operators 4.4. Corresponding Operations on Matrices 4.5. Further Properties of Matrix Multiplication 4.6. The Range and Null Space of a Linear Operator 4.7. Linear Operators Mapping a Space Kn into Itself 4.8. Invariant Subspaces 4.9. Eigenvectors and Eigenvalues Problems chapter 5 COORDINATE TRANSFORMATIONS 5.1. Transformation to a New Basis 5.2. Consecutive Transformations 5.3. Transformation of the Components of a Vector 5.4. Transformation of the Coefficients of a Linear Form 5.5. Transformation of the Matrix of a Linear Operator *5.6. Tensors Problems chapter 6 THE CANONICAL FORM OF THE MATRIX OF A LINEAR OPERATOR 6.1. Canonical Form of the Matrix of a Nilpotent Operator 6.2. Algebras. The Algebra of Polynomials 6.3. Canonical Form of the Matrix of an Arbitrary Operator 6.4. Elementary Divisors 6.5. Further Implications 6.6. The Real Jordan Canonical Form *6.7. "Spectra, Jets and Polynomials" *6.8. Operator Functions and Their Matrices Problems chapter 7 BILINEAR AND QUADRATIC FORMS 7.1. Bilinear Forms 7.2. Quadratic Forms 7.3. Reduction of a Quadratic Form to Canonical Form 7.4. The Canonical Basis of a Bilinear Form 7.5. Construction of a Canonical Basis by Jacobi's Method 7.6. Adjoint Linear Operators 7.7. Isomorphism of Spaces Equipped with a Bilinear Form *7.8. Multilinear Forms 7.9. Bilinear and Quadratic Forms in a Real Space Problems chapter 8 EUCLIDEAN SPACES 8.1. Introduction 8.2. Definition of a Euclidean Space 8.3. Basic Metric Concepts 8.4. Orthogonal Bases 8.5. Perpendiculars 8.6. The Orthogonalization Theorem 8.7. The Gram Determinant 8.8. Incompatible Systems and the Method of Least Squares 8.9. Adjoint Operators and Isometry Problems chapter 9 UNITARY SPACES 9.1. Hermitian Forms 9.2. The Scalar Product in a Complex Space 9.3. Normal Operators 9.4. Applications to Operator Theory in Euclidean Space Problems chapter 10 QUADRATIC FORMS IN EUCLIDEAN AND UNITARY SPACES 10.1. Basic Theorem on Quadratic Forms in a Euclidean Space 10.2. Extremal Properties of a Quadratic Form 10.3 Simultaneous Reduction of Two Quadratic Forms 10.4. Reduction of the General Equation of a Quadratic Surface 10.5. Geometric Properties of a Quadratic Surface *10.6. Analysis of a Quadric Surface from Its Genearl Equation 10.7. Hermitian Quadratic Forms Problems chapter 11 FINITE-DIMENSIONAL ALGEBRAS AND THEIR REPRESENTATIONS 11.1. More on Algebras 11.2. Representations of Abstract Algebras 11.3. Irreducible Representations and Schur's Lemma 11.4. Basic Types of Finite-Dimensional Algebras 11.5. The Left Regular Representation of a Simple Algebra 11.6. Structure of Simple Algebras 11.7. Structure of Semisimple Algebras 11.8. Representations of Simple and Semisimple Algebras 11.9. Some Further Results Problems *Appendix CATEGORIES OF FINITE-DIMENSIONAL SPACES A.1. Introduction A.2. The Case of Complete Algebras A.3. The Case of One-Dimensional Algebras A.4. The Case of Simple Algebras A.5. The Case of Complete Algebras of Diagonal Matrices A.6. Categories and Direct Sums HINTS AND ANSWERS BIBLIOGRAPHY INDEX

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Book by Shilov Georgi E

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Georgi E. Shilov
Editore: Dover Publications Inc., United States (1978)
ISBN 10: 048663518X ISBN 13: 9780486635187
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Descrizione libro Dover Publications Inc., United States, 1978. Paperback. Condizione libro: New. New edition. 208 x 142 mm. Language: English . Brand New Book. In this volume in his exceptional series of translations of Russian mathematical texts, Richard Silverman has taken Shilov s course in linear algebra and has made it even more accessible and more useful for English language readers. Georgi E. Shilov, Professor of Mathematics at the Moscow State University, 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 algebras and their representations, with an appendix on categories of finite-dimensional spaces. The author begins with elementary material and goes easily into the advanced areas, covering all the standard topics of an advanced undergraduate or beginning graduate course. The material is presented in a consistently clear style. Problems are included, with a full section of hints and answers in the back. Keeping in mind the unity of algebra, geometry and analysis in his approach, and writing practically for the studentwho needs to learn techniques, Professor Shilov has produced one of the best expositions on the subject. Because it contains an abundance of problems and examples, the book will be useful for self-study as well as for the classroom. Codice libro della libreria AA99780486635187

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Descrizione libro Dover Pubns, 1977. PAP. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Codice libro della libreria V0-9780486635187

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Georgi E. Shilov
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ISBN 10: 048663518X ISBN 13: 9780486635187
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Descrizione libro Dover Publications Inc., United States, 1978. Paperback. Condizione libro: New. New edition. 208 x 142 mm. Language: English . Brand New Book. In this volume in his exceptional series of translations of Russian mathematical texts, Richard Silverman has taken Shilov s course in linear algebra and has made it even more accessible and more useful for English language readers. Georgi E. Shilov, Professor of Mathematics at the Moscow State University, 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 algebras and their representations, with an appendix on categories of finite-dimensional spaces. The author begins with elementary material and goes easily into the advanced areas, covering all the standard topics of an advanced undergraduate or beginning graduate course. The material is presented in a consistently clear style. Problems are included, with a full section of hints and answers in the back. Keeping in mind the unity of algebra, geometry and analysis in his approach, and writing practically for the studentwho needs to learn techniques, Professor Shilov has produced one of the best expositions on the subject. Because it contains an abundance of problems and examples, the book will be useful for self-study as well as for the classroom. Codice libro della libreria AA99780486635187

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Georgi E. Shilov
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Descrizione libro 1977. Paperback. Condizione libro: New. New edition. 143mm x 20mm x 213mm. Paperback. 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, b.Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 400 pages. 0.413. Codice libro della libreria 9780486635187

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Georgi E. Shilov
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Descrizione libro Dover Publications. Paperback. Condizione libro: New. Paperback. 400 pages. Dimensions: 8.2in. x 5.6in. x 0.8in.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. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Codice libro della libreria 9780486635187

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Georgi-I Evg Shilov
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Descrizione libro Paperback. Condizione libro: BRAND NEW. BRAND NEW. Fast Shipping. Prompt Customer Service. Satisfaction guaranteed. Codice libro della libreria 048663518XBNA

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Georgi E. Shilov
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Descrizione libro Dover Publications Inc., 1978. PAP. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria H8-9780486635187

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Georgi E. Shilov
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Descrizione libro Dover Publications Inc., New York. paperback. Condizione libro: New. Codice libro della libreria 9780486635187

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Georgi Shilov, (Translator) Richard A. Silverman
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Descrizione libro Dover Publications, Inc., 1977. PaperBack. Condizione libro: New. Codice libro della libreria 2066527

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