Week 1: Introduction to Matrix Algebra (01/12/2023)

Ozlem Tuncel

otuncelgurlek1@gsu.edu

⚠️ CAUTION: DO NOT SOLELY RELY ON MY NOTES. THERE MIGHT BE TYPOS AND MISTAKES. ALWAYS TAKE YOUR NOTES!

✔️ The goal of this week is to familiarize yourselves with a few basic math concepts that will help us in OLS. These concepts are:

• matrix/linear algebra
• statistic vs parameter
• vector and scalar

Here are some key points:

• matrix algebra (or linear algebra) is like learning a new language. So, it can be challenging at first, but practice is important.
• a scalar is a single number or constant
• a vector is a matrix but it is just one row and one column
• a matrix has more than one column or row (of vectors)
• a parameter - measurement of population quantities. We cannot directly observe it. It helps us to represent entire population – true unknown/value in the population. Sometimes, it is theoretically possible to know this value but practically nearly impossible. We use greek letters to denote parameters, such as $\mu$ or $\delta$. We cannot ever get the parameter; we can only estimate it using statistics.
• a statistic - measurement of the sample qualities. Basically, this is a way of giving your best guess about some data (e.g., mean of a sample).
• special matrices (e.g., square matrix, symmetric matrix) are important in some instances because you have to have certain types of matrices to perform certain operations. We will talk about them more in upcoming weeks.
• an inverse of matrix is a matrix, and the product between a matrix and its inverse yields to an identity matrix

Some recommendations:

• Definitely go over your notes and practice matrix operations (otherwise you will forget notation and nomenclature)
• Get familiar with concepts like parameter, scalar, vector, etc.
• Get familiar with Greek letters
• If you want more math (yey! 💥), I recommend Math Refresher for Political Scientist - this is a math camp at Harvard’s Department of Government led by Gary King.