Some linear algebra for econometrics
In econometrics, getting a deep understanding of concepts often requires learning some abstract linear algebra. For example, the mathematical properties of ordinary least squares are easier to understand once you know the projection theorem.
As an instructor in the Harvard Economics math camp in August 2019, I prepared notes to help fill in this background. They most useful if you have taken abstract math and the basics of linear algebra, but didn’t take (or don’t really remember) 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 they are the basic prerequisites of the Harvard first-year econometrics course. Other econometrics courses will use these topics differently. In addition, these notes do not replace a course in linear algebra: they have no proofs, few examples, and no computational details.