Why isn't the scaling matrix in LDA normalized?

edit

The scaling matrix in LDA is not normalized because its purpose is to maximize the between-class variability while minimizing the within-class variability. Normalizing the scaling matrix would change its magnitude and alter its ability to achieve this objective. Additionally, the scaling matrix is not unique, as any scalar multiple of the matrix would also achieve the same objective. Therefore, normalization of the scaling matrix is not necessary for achieving the desired results in LDA.