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Linear Algebra for Economists / by Fuad Aleskerov, Hasan Ersel, Dmitri Piontkovski
Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Springer Texts in Business and Economics | SpringerLink BücherPublisher: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2011Description: Online-Ressource (XII, 279p. 65 illus, digital)ISBN:- 9783642205705
- 330.0151
- 330
- 330.1 23
- 512.502433
- HB144
- HB1-846.8
- QA184.2
Contents:
Summary: Some Basic Concepts -- Vectors and Matrices -- Square Matrices and Determinants -- Inverse Matrix -- Systems of Linear Equations -- Linear Spaces -- Euclidean Spaces -- Linear Transformations -- Eigenvectors and Eigenvalues -- Linear Model of Production in a Classical Setting -- Linear Programming -- Natural Numbers and Induction -- Methods of Evaluating Determinants -- Complex Numbers -- Pseudoinverse -- Answers and SolutionsSummary: This textbook introduces students of economics to the fundamental notions and instruments in linear algebra. Linearity is used as a first approximation to many problems that are studied in different branches of science, including economics and other social sciences. Linear algebra is also the most suitable to teach students what proofs are and how to prove a statement. The proofs that are given in the text are relatively easy to understand and also endow the student with different ways of thinking in making proofs. Theorems for which no proofs are given in the book are illustrated via figures and examples. All notions are illustrated appealing to geometric intuition. The book provides a variety of economic examples using linear algebraic tools. It mainly addresses students in economics who need to build up skills in understanding mathematical reasoning. Students in mathematics and informatics may also be interested in learning about the use of mathematics in economicsPPN: PPN: 1651021031Package identifier: Produktsigel: ZDB-2-SBE
""Linear Algebra for Economists ""; ""Preface""; ""Acknowledgements""; ""Contents ""; ""1 Some Basic Concepts""; ""1.1 Introduction""; ""1.1.1 Linearity""; ""1.1.2 System of Coordinates on the Plane R2""; ""1.2 Microeconomics: Market Equilibrium""; ""1.2.1 Equilibrium in a Single Market""; ""1.2.2 Multi-Market Equilibrium""; ""1.3 Macroeconomic Policy Problem""; ""1.3.1 A Simple Macroeconomic Policy Modelwith One Target""; ""1.3.2 A Macroeconomic Policy Modelwith Multiple Targets and Multiple Instruments""; ""1.4 Problems""; ""2 Vectors and Matrices""; ""2.1 Vectors""
""2.1.1 Algebraic Properties of Vectors""""2.1.2 Geometric Interpretation of Vectorsand Operations on Them""; ""2.1.3 Geometric Interpretation in R2""; ""2.2 Dot Product of Two Vectors""; ""2.2.1 The Length of a Vector, and the AngleBetween Two Vectors""; ""2.3 An Economic Example: Two Plants""; ""2.4 Another Economic Application: Index Numbers""; ""2.5 Matrices""; ""2.5.1 Operations on Matrices""; ""2.5.2 Matrix Multiplication""; ""2.5.3 Trace of a Matrix""; ""2.6 Transpose of a Matrix""; ""2.7 Rank of a Matrix""; ""2.8 Elementary Operations and Elementary Matrices""; ""2.9 Problems""
""3 Square Matrices and Determinants""""3.1 Transformation of Coordinates""; ""3.1.1 Translation""; ""3.1.2 Rotation""; ""3.2 Square Matrices""; ""3.2.1 Identity Matrix""; ""3.2.2 Power of a Matrix and Polynomial of a Matrix""; ""3.3 Systems of Linear Equations: The Case of Two Variables""; ""3.4 Determinant of a Matrix""; ""3.4.1 The Basic Properties of Determinants""; ""3.4.2 Determinant and Elementary Operations""; ""3.5 Problems""; ""4 Inverse Matrix""; ""4.1 Inverse Matrix and Matrix Division""; ""4.2 Rank and Determinants""; ""4.3 Problems""; ""5 Systems of Linear Equations""
""5.1 The Case of Unique Solution: Cramer's Rule""""5.2 Gauss Method: Sequential Elimination of Unknown Variables""; ""5.3 Homogeneous Equations""; ""5.4 Problems""; ""5.4.1 Mathematical Problems""; ""5.4.2 Economic Problems""; ""6 Linear Spaces""; ""6.1 Linear Independence of Vectors""; ""6.1.1 Addition of Vectors and Multiplicationof a Vector by a Real Number""; ""6.2 Isomorphism of Linear Spaces""; ""6.3 Subspaces""; ""6.3.1 Examples of Subspaces""; ""6.3.2 A Method of Constructing Subspaces""; ""6.3.3 One-Dimensional Subspaces""; ""6.3.4 Hyperplane""; ""6.4 Coordinate Change""
""6.5 Economic Example: Production Technology Set""""6.6 Problems""; ""7 Euclidean Spaces""; ""7.1 General Definitions""; ""7.2 Orthogonal Bases""; ""7.3 Least Squares Method""; ""7.4 Isomorphism of Euclidean Spaces""; ""7.5 Problems""; ""8 Linear Transformations""; ""8.1 Addition and Multiplication of Linear Operators""; ""8.2 Inverse Transformation, Image and Kernelunder a Transformation""; ""8.3 Linear Transformation Matrices with Respectto Different Bases""; ""8.4 Problems""; ""9 Eigenvectors and Eigenvalues""; ""9.1 Macroeconomic Example: Growth and Consumption""; ""9.1.1 The Model""
""9.1.2 Numerical Example""
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