298,03 zł

Representation Theory Springer-Verlag New York Inc.

Książki / Literatura obcojęzyczna

Introducing finite-dimensional representations of Lie groups and Lie algebras, this example-oriented book works from representation theory of finite groups, through Lie groups and Lie algrbras to the finite dimensional representations of the classical groups.

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103,61 zł

Linear Algebra Dover Publications Inc.

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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 Problemschapter 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 Problemschapter 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 Problemschapter 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 Problemschapter 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 Problemschapter 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 Problemschapter 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 Problemschapter 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 Problemschapter 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 Problemschapter 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 Problemschapter 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 SumsHINTS AND ANSWERSBIBLIOGRAPHYINDEX

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50,91 zł

Death of Money Penguin Books

Książki / Literatura obcojęzyczna

Presents a collection of research papers and survey articles that reflects the interplay of finite-dimensional algebras with other areas (algebraic geometry, homological algebra, and the theory of quantum groups). This work features several expository articles which introduce the beginning researcher to topics in representation theory.

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467,87 zł

From Special Relativity to Feynman Diagrams Springer International Publishing AG

Książki / Literatura obcojęzyczna

This book, now in its second edition, provides an introductory course on theoretical particle physics with the aim of filling the gap that exists between basic courses of classical and quantum mechanics and advanced courses of (relativistic) quantum mechanics and field theory. After a concise but comprehensive introduction to special relativity, key aspects of relativistic dynamics are covered and some elementary concepts of general relativity introduced. Basics of the theory of groups and Lie algebras are explained, with discussion of the group of rotations and the Lorentz and Poincaré groups. In addition, a concise account of representation theory and of tensor calculus is provided. Quantization of the electromagnetic field in the radiation range is fully discussed. The essentials of the Lagrangian and Hamiltonian formalisms are reviewed, proceeding from systems with a finite number of degrees of freedom and extending the discussion to fields. The final four chapters are devoted to development of the quantum field theory, ultimately introducing the graphical description of interaction processes by means of Feynman diagrams. The book will be of value for students seeking to understand the main concepts that form the basis of contemporary theoretical particle physics and also for engineers and lecturers. An Appendix on some special relativity effects is added.

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343,03 zł

From Special Relativity to Feynman Diagrams Springer International Publishing AG

Książki / Literatura obcojęzyczna

This book, now in its second edition, provides an introductory course on theoretical particle physics with the aim of filling the gap that exists between basic courses of classical and quantum mechanics and advanced courses of (relativistic) quantum mechanics and field theory. After a concise but comprehensive introduction to special relativity, key aspects of relativistic dynamics are covered and some elementary concepts of general relativity introduced. Basics of the theory of groups and Lie algebras are explained, with discussion of the group of rotations and the Lorentz and Poincaré groups. In addition, a concise account of representation theory and of tensor calculus is provided. Quantization of the electromagnetic field in the radiation range is fully discussed. The essentials of the Lagrangian and Hamiltonian formalisms are reviewed, proceeding from systems with a finite number of degrees of freedom and extending the discussion to fields. The final four chapters are devoted to development of the quantum field theory, ultimately introducing the graphical description of interaction processes by means of Feynman diagrams. The book will be of value for students seeking to understand the main concepts that form the basis of contemporary theoretical particle physics and also for engineers and lecturers. An Appendix on some special relativity effects is added.

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