What is the difference between linear discriminant analysis and quadrant discriminant analysis?

In my last post I discussed the difference between logistic regression and linear discriminant analysis, and that blog post can be found here:- https://tracyrenee61.medium.com/what-is-the-difference-between-linear-discriminant-analysis-and-logistic-regression-d1dd1cdd985b

During my research, I noted that in addition to linear discriminant analysis, there is another multivariate model, quadratic discriminant analysis, and decided that an analysis of these two multivariate statistical models is warranted.

Covariance matrix

A covariance matrix is central to understanding discriminant analysis, as it captures the relationships between variables within your data.

In statistics, a covariance matrix is a square matrix that displays the covariances between each pair of variables in a dataset. If you have p variables, the covariance matrix will be a p times p matrix. The diagonal elements represent the variances of individual variables, while the off-diagonal elements represent the covariances between pairs of variables.

Discriminant analysis, like Linear Discriminant Analysis (LDA), works to find the linear combinations of variables that best separate predefined groups or classes in your…