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Linear Algebra for Economists 2011th Edition by Hasan Ersel, Dmitri Piontkovski ISBN 3642205704 9783642205705

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ISBN 10:    3642205704
ISBN 13: 978-3642205705
Author:       Hasan Ersel, Dmitri Piontkovski

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 economics.
 

 Linear Algebra for Economists 2011th Table of contents:

Chapter 1: Basic Concepts of Linear Algebra

  1. Vectors and Matrices

    • Definition and Basic Operations
    • Vector Addition and Scalar Multiplication
    • Matrix Operations (Addition, Multiplication)
    • Transpose of a Matrix

  2. Systems of Linear Equations

    • Solving Systems of Linear Equations
    • Gaussian Elimination and Matrix Formulation

  3. Determinants

    • Definition and Properties of Determinants
    • The Role of Determinants in Solving Linear Systems

Chapter 2: Vector Spaces and Linear Independence

  1. Vector Spaces

    • Definition of a Vector Space
    • Subspaces and Spanning Sets
    • Basis and Dimension

  2. Linear Independence

    • Linear Independence of Vectors
    • Rank of a Matrix
    • Rank-Nullity Theorem

Chapter 3: Eigenvalues and Eigenvectors

  1. Eigenvalues and Eigenvectors

    • Definition and Computation
    • Characteristic Equation
    • Diagonalization of Matrices

  2. Applications in Economics

    • Solving Systems of Differential Equations
    • Stability Analysis and Growth Models

Chapter 4: Matrix Decompositions and Applications

  1. Matrix Factorizations

    • LU Decomposition
    • QR Decomposition
    • Singular Value Decomposition (SVD)

  2. Applications in Economics

    • Input-Output Models
    • Optimization Problems

Chapter 5: Linear Transformations

  1. Linear Maps and Transformations

    • Definition and Examples of Linear Transformations
    • The Matrix Representation of Linear Maps

  2. Applications to Economics

    • Economic Modeling and Transformation of Variables

Chapter 6: Advanced Topics in Linear Algebra

  1. Positive Definite Matrices

    • Definition and Properties
    • Applications in Optimization

  2. Least Squares and Regression Analysis

    • Linear Regression via Least Squares
    • Econometric Applications

Chapter 7: Optimization and Linear Programming

  1. Linear Programming
    • The Simplex Method
    • Duality in Linear Programming
    • Economic Applications of Linear Programming

Chapter 8: Systems of Dynamic Equations and Stability Analysis

  1. Difference Equations and Stability

    • Dynamic Systems and Eigenvalue Analysis
    • Stability Conditions for Economic Models

  2. Applications in Economic Growth and Fluctuations

    • Solving Economic Models with Dynamic Systems

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