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دانلود کتاب A First Course in Linear Algebra
دانلود کتاب اولین دوره در جبر خطی
مشخصات کتاب
A First Course in Linear Algebra
ویرایش:
نویسندگان: Robert A Beezer
سری:
ناشر:
سال نشر:
تعداد صفحات: 848
زبان: English
فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود)
حجم فایل: 6 مگابایت
قیمت کتاب (تومان) : 36,000
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توضیحاتی در مورد کتاب اولین دوره در جبر خطی
اولین دوره در جبر خطی، مقدمه ای بر مفاهیم اساسی جبر خطی، همراه با مقدمه ای بر تکنیک های ریاضیات رسمی است. قبل از حرکت به نظریه فضاهای برداری انتزاعی، مقادیر ویژه، تبدیل های خطی و نمایش های ماتریسی، با سیستم های معادلات و جبر ماتریسی شروع می شود. دارای مثال‌ها و تمرین‌های متعدد، همراه با بیان دقیق تعاریف و اثبات کامل هر قضیه است که آن را برای مطالعه مستقل ایده‌آل می‌کند.
توضیحاتی درمورد کتاب به خارجی
A First Course in Linear Algebra is an introduction to the basic concepts of linear algebra, along with an introduction to the techniques of formal mathematics. It begins with systems of equations and matrix algebra before moving into the theory of abstract vector spaces, eigenvalues, linear transformations and matrix representations. It has numerous worked examples and exercises, along with precise statements of definitions and complete proofs of every theorem, making it ideal for independent study.
فهرست مطالب
Preface Contents Definitions Theorems Notation Examples Proof Techniques Computation Notes Contributors GNU Free Documentation License 1. APPLICABILITY AND DEFINITIONS 2. VERBATIM COPYING 3. COPYING IN QUANTITY 4. MODIFICATIONS 5. COMBINING DOCUMENTS 6. COLLECTIONS OF DOCUMENTS 7. AGGREGATION WITH INDEPENDENT WORKS 8. TRANSLATION 9. TERMINATION 10. FUTURE REVISIONS OF THIS LICENSE ADDENDUM: How to use this License for your documents Part C Core Chapter SLE Systems of Linear Equations WILA What is Linear Algebra? LA ``Linear'' + ``Algebra'' A An application: packaging trail mix READ Reading Questions EXC Exercises SOL Solutions SSLE Solving Systems of Linear Equations PSS Possibilities for solution sets ESEO Equivalent systems and equation operations READ Reading Questions EXC Exercises SOL Solutions RREF Reduced Row-Echelon Form READ Reading Questions EXC Exercises SOL Solutions TSS Types of Solution Sets READ Reading Questions EXC Exercises SOL Solutions HSE Homogeneous Systems of Equations SHS Solutions of Homogeneous Systems MVNSE Matrix and Vector Notation for Systems of Equations NSM Null Space of a Matrix READ Reading Questions EXC Exercises SOL Solutions NSM NonSingular Matrices NSM NonSingular Matrices READ Reading Questions EXC Exercises SOL Solutions Chapter V Vectors VO Vector Operations VEASM Vector equality, addition, scalar multiplication VSP Vector Space Properties READ Reading Questions EXC Exercises SOL Solutions LC Linear Combinations LC Linear Combinations VFSS Vector Form of Solution Sets PSHS Particular Solutions, Homogeneous Solutions URREF Uniqueness of Reduced Row-Echelon Form READ Reading Questions EXC Exercises SOL Solutions SS Spanning Sets SSV Span of a Set of Vectors SSNS Spanning Sets of Null Spaces READ Reading Questions EXC Exercises SOL Solutions LI Linear Independence LISV Linearly Independent Sets of Vectors LINSM Linear Independence and NonSingular Matrices NSSLI Null Spaces, Spans, Linear Independence READ Reading Questions EXC Exercises SOL Solutions LDS Linear Dependence and Spans LDSS Linearly Dependent Sets and Spans COV Casting Out Vectors READ Reading Questions EXC Exercises SOL Solutions O Orthogonality CAV Complex arithmetic and vectors IP Inner products N Norm OV Orthogonal Vectors GSP Gram-Schmidt Procedure READ Reading Questions EXC Exercises Chapter M Matrices MO Matrix Operations MEASM Matrix equality, addition, scalar multiplication VSP Vector Space Properties TSM Transposes and Symmetric Matrices MCC Matrices and Complex Conjugation READ Reading Questions EXC Exercises SOL Solutions MM Matrix Multiplication MVP Matrix-Vector Product MM Matrix Multiplication MMEE Matrix Multiplication, Entry-by-Entry PMM Properties of Matrix Multiplication READ Reading Questions EXC Exercises SOL Solutions MISLE Matrix Inverses and Systems of Linear Equations IM Inverse of a Matrix CIM Computing the Inverse of a Matrix PMI Properties of Matrix Inverses READ Reading Questions EXC Exercises SOL Solutions MINSM Matrix Inverses and NonSingular Matrices NSMI NonSingular Matrices are Invertible OM Orthogonal Matrices READ Reading Questions EXC Exercises SOL Solutions CRS Column and Row Spaces CSSE Column spaces and systems of equations CSSOC Column space spanned by original columns CSNSM Column Space of a Nonsingular Matrix RSM Row Space of a Matrix READ Reading Questions EXC Exercises SOL Solutions FS Four Subsets LNS Left Null Space CRS Computing Column Spaces EEF Extended echelon form FS Four Subsets READ Reading Questions EXC Exercises SOL Solutions Chapter VS Vector Spaces VS Vector Spaces VS Vector Spaces EVS Examples of Vector Spaces VSP Vector Space Properties RD Recycling Definitions READ Reading Questions EXC Exercises S Subspaces TS Testing Subspaces TSS The Span of a Set SC Subspace Constructions READ Reading Questions EXC Exercises SOL Solutions LISS Linear Independence and Spanning Sets LI Linear independence SS Spanning Sets VR Vector Representation READ Reading Questions EXC Exercises SOL Solutions B Bases B Bases BSCV Bases for Spans of Column Vectors BNSM Bases and NonSingular Matrices OBC Orthonormal Bases and Coordinates READ Reading Questions EXC Exercises SOL Solutions D Dimension D Dimension DVS Dimension of Vector Spaces RNM Rank and Nullity of a Matrix RNNSM Rank and Nullity of a NonSingular Matrix READ Reading Questions EXC Exercises SOL Solutions PD Properties of Dimension GT Goldilocks' Theorem RT Ranks and Transposes DFS Dimension of Four Subspaces READ Reading Questions EXC Exercises SOL Solutions Chapter D Determinants DM Determinants of Matrices EM Elementary Matrices DD Definition of the Determinant CD Computing Determinants READ Reading Questions EXC Exercises SOL Solutions PDM Properties of Determinants of Matrices DRO Determinants and Row Operations DROEM Determinants, Row Operations, Elementary Matrices DNMMM Determinants, Nonsingular Matrices, Matrix Multiplication READ Reading Questions EXC Exercises SOL Solutions Chapter E Eigenvalues EE Eigenvalues and Eigenvectors EEM Eigenvalues and Eigenvectors of a Matrix PM Polynomials and Matrices EEE Existence of Eigenvalues and Eigenvectors CEE Computing Eigenvalues and Eigenvectors ECEE Examples of Computing Eigenvalues and Eigenvectors READ Reading Questions EXC Exercises SOL Solutions PEE Properties of Eigenvalues and Eigenvectors ME Multiplicities of Eigenvalues EHM Eigenvalues of Hermitian Matrices READ Reading Questions EXC Exercises SOL Solutions SD Similarity and Diagonalization SM Similar Matrices PSM Properties of Similar Matrices D Diagonalization OD Orthonormal Diagonalization READ Reading Questions EXC Exercises SOL Solutions Chapter LT Linear Transformations LT Linear Transformations LT Linear Transformations MLT Matrices and Linear Transformations LTLC Linear Transformations and Linear Combinations PI Pre-Images NLTFO New Linear Transformations From Old READ Reading Questions EXC Exercises SOL Solutions ILT Injective Linear Transformations EILT Examples of Injective Linear Transformations KLT Kernel of a Linear Transformation ILTLI Injective Linear Transformations and Linear Independence ILTD Injective Linear Transformations and Dimension CILT Composition of Injective Linear Transformations READ Reading Questions EXC Exercises SOL Solutions SLT Surjective Linear Transformations ESLT Examples of Surjective Linear Transformations RLT Range of a Linear Transformation SSSLT Spanning Sets and Surjective Linear Transformations SLTD Surjective Linear Transformations and Dimension CSLT Composition of Surjective Linear Transformations READ Reading Questions EXC Exercises SOL Solutions IVLT Invertible Linear Transformations IVLT Invertible Linear Transformations IV Invertibility SI Structure and Isomorphism RNLT Rank and Nullity of a Linear Transformation SLELT Systems of Linear Equations and Linear Transformations READ Reading Questions EXC Exercises SOL Solutions Chapter R Representations VR Vector Representations CVS Characterization of Vector Spaces CP Coordinatization Principle READ Reading Questions EXC Exercises SOL Solutions MR Matrix Representations NRFO New Representations from Old PMR Properties of Matrix Representations IVLT Invertible Linear Transformations READ Reading Questions EXC Exercises SOL Solutions CB Change of Basis EELT Eigenvalues and Eigenvectors of Linear Transformations CBM Change-of-Basis Matrix MRS Matrix Representations and Similarity CELT Computing Eigenvectors of Linear Transformations READ Reading Questions EXC Exercises SOL Solutions Chapter A Archetypes A B C D E F G H I J K L M N O P Q R S T U V W Part T Topics Chapter P Preliminaries CNO Complex Number Operations CNA Arithmetic with complex numbers CCN Conjugates of Complex Numbers MCN Modulus of a Complex Number Part A Applications
