Mathematical Foundation of Economic Management Discipline: Linear Algebra

Author: Lu Gang
Publisher:
Publish Date: 2003-05-01
Features: This book is a research outcome of the "Reform Plan for Teaching Content and Curriculum System in Higher Education Towards the 21st Century" by the Ministry of Education. It is one of the mathematical foundation textbooks for economics and management disciplines in higher education institutions. The book introduces matrices, systems of linear equations, linear spaces and linear transformations, eigenvalues and eigenvectors of matrices, and quadratic forms in a scientific and systematic manner, using a way that is easily acceptable to business and economics students. It focuses on the application of theories and methods, as well as the introduction of economic and mathematical models, and includes exercises with reference answers. The content arrangement of the book also considers the needs of business and economics students for postgraduate entrance exams, making it suitable for students preparing for such exams as well.
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Chapter 1 Matrices
§1.1 Concept of Matrices
§1.2 Matrix Operations
§1.3 Determinants of Square Matrices
§1.4 Matrix Blocking
§1.5 Invertible Matrices
§1.6 Elementary Row Operations of Matrices
§1.7 Rank of Matrices
§1.8 Two Examples of Matrix Applications
Exercises 1
Chapter 2 Systems of Linear Equations
§2.1 Systems of Linear Equations
§2.2 Vectors and Their Linear Operations
§2.3 Linear Relationships Between Vectors
§2.4 Rank of a Vector Set
§2.5 Structure of Solutions to Linear Equations
§2.6 Standard Orthogonal Basis of R^n
Exercises 2
Chapter 3 Linear Spaces and Linear Transformations
§3.1 Linear Spaces
§3.2 Linear Transformations
§3.3 Introduction to Euclidean Spaces
Exercises
Chapter 4 Eigenvalues and Eigenvectors of Matrices
§4.1 Eigenvalues and Eigenvectors of Matrices
§4.2 Similar Matrices and Conditions for Diagonalizability
§4.3 Eigenvalues and Eigenvectors of Real Symmetric Matrices
§4.4 Matrix Series
§4.5 Applications (I)
§4.6 Applications (II) - Introduction to Input-Output Analysis
Exercises 4
Chapter 5 Quadratic Forms
§5.1 Basic Concepts
§5.2 Standard and Normal Forms of Quadratic Forms
§5.3 Definiteness of Quadratic Forms and Symmetric Matrices
§5.4 Applications of Positive Definite Matrices
Exercises 5
Exercises Hints and Reference Answers
References