Intuition for why LDA is a special case of naive Bayes The naive Bayes classifier assumes the regressors to be mutually independent, while linear discriminant analysis (LDA) allows them to be correlated. James et al. "An Introduction to Statistical Learning" (2nd edition, 2021) section 4.5 (bottom of p. 159) claim that LDA is in fact a special case of the naive Bayes classifier (admitting that the fact is not at all obvious -- with which I agree, and hence my question). What is the intuition?

Here's my intuition:
The LDA classifier assumes that across all classes, the $p$ predictors $\boldsymbol{X}_k$ (for $k=1, \dots,p$) all share some covariance matrix ${\boldsymbol \Sigma}$, but may have different means $\boldsymbol{\mu}_k$. Thus, if you define the alternate set of predictors $\boldsymbol{Z}$ to be $p$ independent normal random variables with variance 1 and means $\boldsymbol{\Sigma}^{-1/2} \boldsymbol{\mu}$, then $\boldsymbol{X} = \boldsymbol{\Sigma}^{1/2} \boldsymbol{Z}$. This is a linear transformation, so a linear classifier on the $\boldsymbol{Z}$ variables would be linear on the $\boldsymbol{X}$ variables, too.
Note that the naive Bayes classifier is linear on its predictors (this is shown on page 159 of your reference), and it clearly applies on the $\boldsymbol{Z}$ predictors since they are independent by definition. So LDA is the same as some naive Bayes classifier. But as mentioned in your reference (also page 159), the same is true of any linear classifier.
