# Crash Course on Input-Output Model Mathematics

#### Summary

A brief review of the linear algebra and matrix theory concepts underpinning standard environmentally extended input-output models.

#### Content

This brief introduction in Input-Output Model mathematics discusses the basic elements of linear algebra that are necessary to understand the standard Input-Output models, including their Environmental impact extensions.

Matrix theory is the main subject covered here as it is the most dominant mathematical tool used in this area (though other parts of mathematics do find applications in Input-Output analysis). The focus is on the notation and mathematical objects commonly used, not the economic interpretation or any mathematical proofs.

This resource can be seen a slightly more mathematical version of Appendix A, Matrix Algebra for Input–Output Models of the book Input-Output Analysis Foundations and Extensions by Miller and Blair. It follows roughly the naming, notation and conventions of the Encyclopedic Dictionary of Mathematics. The course should be useful for people who want to refresh their linear algebra and matrix theory knowledge or identify specific areas they need to study deeper.

A summary of the main topics covered:

- Basics
- Matrix Definition
- Matrix Families
- Matrix Operations
- Matrix-Matrix Multiplication
- Matrix Inversion
- Matrix Series
- IO Specific Topics

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