A new crash course is available now in the Academy.

The course should be useful for people who want to refresh their linear algebra and matrix theory knowledge or want identify specific areas which they wish to study deeper. It offers a brief introduction to **Input-Output Model mathematics**, the basic elements of linear algebra and matrix theory 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 dominant mathematical tool used in IO analysis. The focus is on notation and defining the mathematical objects and operations commonly used, not the economic interpretation or any mathematical proofs.

This resource can be seen as a slightly more mathematical version compared to Appendix A: Matrix Algebra for Input-Output Models as presented in the definitive textbook on IO models, namely **Input-Output Analysis Foundations and Extensions by Miller and Blair**. We follow roughly the naming, notation and conventions of the **Encyclopedic Dictionary of Mathematics**.

A summary of the main topics covered:

- Basics, Matrix Definition, Matrix Families
- Various Matrix Operations
- Matrix-Matrix Products (Cayley, Hadamard, Kronecker etc.)
- Matrix Inversion and Matrix Series
- Select IO Specific Topics

You can enroll directly here. Enjoy and keep us posted with any observations, ideas or feedback on how to improve this resource.