In "between-class" scatter matrix, what does "overall mean" $m$ refer to?
Because the formulation is
$$\sum_{i=1}^c N_i (m_i - m) (m_i - m)^T$$
where $N_i$s is the size of $i$th sample (each column is a sample), $m_i$ is the sample mean of $i$th sample. But what does $m$, the overall mean, refer to?
Let $N$ be the total number of observations, and $N_i$ the number of observation in $i$th class. Total of $c$ classes, hence the overall mean is
$$ m = \frac{1}{N}\sum_{i=1}^c \sum_{j=1}^{N_i} m_{ij} , $$ where $m_{ij}$ is the $j$th observation from $i$th class.