Some linear algebra for econometrics
Students of econometrics who want to learn concepts more deeply are often confronted by the need to know some abstract linear algebra. This is especially the case in econometrics courses that emphasize the mathematical properties of ordinary least squares.
As an instructor in the Harvard Economics math camp in August 2019, I prepared notes to help with this problem. They are aimed at students who are familiar with abstract math, but have not taken (or may not remember) much abstract linear algebra or functional analysis.
They cover the following linear algebra topics:
- Vector space preliminaries, including basis and dimension
- Linear transformations and matrix basics
- Trace, determinant, and eigenvalues
- Inner products and orthogonality
- Projections and the classical projection theorem
- Basic matrix decompositions: singular value and Cholesky
- The Kronecker tensor product
These topics were chosen because of the specific requirements of the Harvard first-year course. Different presentations of econometrics will use these topics differently. In addition, these notes do not replace a good course in linear algebra: they have no proofs, few examples, and no computational details.