What This Document Is
This document presents detailed lecture text from an introductory economics course (ECON 2) at the University of California, Berkeley. Specifically, it delves into the foundational mathematical concepts underpinning economic theory – linear algebra. It’s designed to provide a rigorous exploration of vector spaces, building from basic definitions to more complex theorems. This material forms a crucial building block for understanding advanced economic modeling and analysis.
Why This Document Matters
This resource is ideal for students enrolled in introductory economics courses that utilize a mathematical approach. It’s particularly beneficial for those who want a comprehensive and detailed record of the lecture material, allowing for focused review and deeper understanding. Students preparing for exams, working through problem sets, or seeking to solidify their grasp of linear algebra as applied to economics will find this document exceptionally valuable. Access to the full content will empower you to confidently navigate the mathematical foundations of economic principles.
Topics Covered
* Linear Combinations and Spans
* Linear Dependence and Independence
* Hamel Bases and Basis Properties
* Cardinality of Bases
* Vector Space Foundations
* Representation of Vectors within a Basis
* The Axiom of Choice and its relation to basis existence
What This Document Provides
* Precise definitions of key linear algebra concepts.
* A structured outline mirroring a university lecture format.
* Theoretical statements (Theorems) relating to vector spaces and bases.
* Detailed explanations building from fundamental principles.
* A foundation for understanding more advanced economic models.
* A rigorous treatment of the mathematical underpinnings of economic theory.
