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دانلود کتاب Linear Algebra Done Right
دانلود کتاب جبر خطی درست انجام شد
مشخصات کتاب
Linear Algebra Done Right
ویرایش: 4
نویسندگان: Sheldon Axler
سری: Undergraduate Texts in Mathematics
ISBN (شابک) : 3031410254, 9783031410260
ناشر: Springer
سال نشر: 2023
تعداد صفحات: 408
زبان: English
فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود)
حجم فایل: 7 مگابایت
قیمت کتاب (تومان) : 78,000
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توضیحاتی درمورد کتاب به خارجی
فهرست مطالب
About the Author Contents Preface for Students Preface for Instructors The author’s top ten Major improvements and additions for the fourth edition Acknowledgments Chapter 1 Vector Spaces 1A Rⁿ and Cⁿ Complex Numbers Lists Fⁿ Digression on Fields Exercises 1A 1B Definition of Vector Space Exercises 1B 1C Subspaces Sums of Subspaces Direct Sums Exercises 1C Chapter 2 Finite-Dimensional Vector Spaces 2A Span and Linear Independence Linear Combinations and Span Linear Independence Exercises 2A 2B Bases Exercises 2B 2C Dimension Exercises 2C Chapter 3 Linear Maps 3A Vector Space of Linear Maps Definition and Examples of Linear Maps Algebraic Operations on L(V, W) Exercises 3A 3B Null Spaces and Ranges Null Space and Injectivity Range and Surjectivity Fundamental Theorem of Linear Maps Exercises 3B 3C Matrices Representing a Linear Map by a Matrix Addition and Scalar Multiplication of Matrices Matrix Multiplication Column–Row Factorization and Rank of a Matrix Exercises 3C 3D Invertibility and Isomorphisms Invertible Linear Maps Isomorphic Vector Spaces Linear Maps Thought of as Matrix Multiplication Change of Basis Exercises 3D 3E Products and Quotients of Vector Spaces Products of Vector Spaces Quotient Spaces Exercises 3E 3F Duality Dual Space and Dual Map Null Space and Range of Dual of Linear Map Matrix of Dual of Linear Map Exercises 3F Chapter 4 Polynomials Zeros of Polynomials Division Algorithm for Polynomials Factorization of Polynomials over C Factorization of Polynomials over R Exercises 4 Chapter 5 Eigenvalues and Eigenvectors 5A Invariant Subspaces Eigenvalues Polynomials Applied to Operators Exercises 5A 5B The Minimal Polynomial Existence of Eigenvalues on Complex Vector Spaces Eigenvalues and the Minimal Polynomial Eigenvalues on Odd-Dimensional Real Vector Spaces Exercises 5B 5C Upper-Triangular Matrices Exercises 5C 5D Diagonalizable Operators Diagonal Matrices Conditions for Diagonalizability Gershgorin Disk Theorem Exercises 5D 5E Commuting Operators Exercises 5E Chapter 6 Inner Product Spaces 6A Inner Products and Norms Inner Products Norms Exercises 6A 6B Orthonormal Bases Orthonormal Lists and the Gram–Schmidt Procedure Linear Functionals on Inner Product Spaces Exercises 6B 6C Orthogonal Complements and Minimization Problems Orthogonal Complements Minimization Problems Pseudoinverse Exercises 6C Chapter 7 Operators on Inner Product Spaces 7A Self-Adjoint and Normal Operators Adjoints Self-Adjoint Operators Normal Operators Exercises 7A 7B Spectral Theorem Real Spectral Theorem Complex Spectral Theorem Exercises 7B 7C Positive Operators Exercises 7C 7D Isometries, Unitary Operators, and Matrix Factorization Isometries Unitary Operators QR Factorization Cholesky Factorization Exercises 7D 7E Singular Value Decomposition Singular Values SVD for Linear Maps and for Matrices Exercises 7E 7F Consequences of Singular Value Decomposition Norms of Linear Maps Approximation by Linear Maps with Lower-Dimensional Range Polar Decomposition Operators Applied to Ellipsoids and Parallelepipeds Volume via Singular Values Properties of an Operator as Determined by Its Eigenvalues Exercises 7F Chapter 8 Operators on Complex Vector Spaces 8A Generalized Eigenvectors and Nilpotent Operators Null Spaces of Powers of an Operator Generalized Eigenvectors Nilpotent Operators Exercises 8A 8B Generalized Eigenspace Decomposition Generalized Eigenspaces Multiplicity of an Eigenvalue Block Diagonal Matrices Exercises 8B 8C Consequences of Generalized Eigenspace Decomposition Square Roots of Operators Jordan Form Exercises 8C 8D Trace: A Connection Between Matrices and Operators Exercises 8D Chapter 9 Multilinear Algebra and Determinants 9A Bilinear Forms and Quadratic Forms Bilinear Forms Symmetric Bilinear Forms Quadratic Forms Exercises 9A 9B Alternating Multilinear Forms Multilinear Forms Alternating Multilinear Forms and Permutations Exercises 9B 9C Determinants Defining the Determinant Properties of Determinants Exercises 9C 9D Tensor Products Tensor Product of Two Vector Spaces Tensor Product of Inner Product Spaces Tensor Product of Multiple Vector Spaces Exercises 9D Photo Credits Symbol Index Index Colophon: Notes on Typesetting
