# Why does the Y component in YCbCr represent luma/intensity?

As far as I know, the RGB to YCbCr conversion is just a linear transformation, yet the Y channel successfully captures the intensity value of each pixel. How?

In other words, where do the following magic numbers come from?

\begin{align} E'_Y &= 0.299E'_R + 0.587E'_G + 0.114E'_B \\ E'_R - E'_Y &= 0.701E'_R - 0.587E'_G - 0.114E'_B \\ E'_B - E'_Y &= -0.299E'_R - 0.587E'_G + 0.886E'_B \end{align}