Solved – How to detect if a given dataset has multivariate normal distribution

I'm looking at Fisher's LDA on various datasets on UCI ML repository and trying to see where LDA might perform badly. One reason I can think of is if the data distribution is not a multi-variate normal distribution. This is from the fact I read in a book where you apply LDA on multivariate normal distribution. Is that thought process correct? When might LDA give bad results?

By definition the random vector $X$ is multivariate normal if all linear combinations $a^T X$ have some (univariate) normal distribution. So one idea to test multivariate normality is to search among the vectors $a$ for one such that $a^T X$ is definitely not normal. That is the idea behind pp, projection pursuit methods. See

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