In Gaussian naive bayes when we have more than one features ,then we apply Multivariate Normal Distribution Formula for calculating likelihood,
But in Multivariate Normal Distribution, we have Co-Variance Matrix in which all features may not be independent of each other , but this will violate the assumption of naive bayes Classifier ??
If features are independent of each other that means we have a diagonal matrix of co-Variance Matrix ???
Actually its an assumption of gaussian naive bayes that we assume that features are independent, which actually may not be true. This assumption is just for simplification of the formula for gaussian naive bayes algorithm. If not assumed so, then the formula would not be that easy, and we would face many more difficulties in implementing the algorithm.
So its an assumption, that all features are independent (which may or may not be actually true). So its an assumption that while implementing this algorithm we will assume that only diagnol values exist in covariance matrix and rest all are zero, (which may or may not be actually true).
Hope this helped you. 