Define $$\boldsymbol{\mu}=\frac{1}{N}\sum^N_{i=1}\boldsymbol{x_i}$$ If we have a direction vector $\boldsymbol{w}$, The book stated that the projection of the mean onto the line $\boldsymbol{w}$ is given by: $$ m_k=\boldsymbol{w}^T\boldsymbol{\mu} $$
I don't get this. Isn't the projection of $\mu$ onto $w$ given by:
$$
\boldsymbol{m}=\boldsymbol{w}\frac{\boldsymbol{w}^T\boldsymbol{\mu}}{||\boldsymbol{w}||}
$$
I've attached the part on the book: