= Luma
{disambiguate=video}
{title2=$Y'$}
\b[Luma] is a video signal formed by combining nonlinear <RGB> component signals. It is conventionally written $Y'$, with the prime warning that the components have already undergone a nonlinear encoding. It differs from physical <luminance>, which describes light with a photometric scale.
Under <Recommendation ITU-R BT.709-6>,
$$
Y'=0.2126R'+0.7152G'+0.0722B'.
$$
The coefficients sum to one, so a neutral signal $R'=G'=B'=t$ has luma $Y'=t$. The same recommendation specifies a nonlinear conversion $f$ from a normalized linear primary signal $E$:
$$
f(E)=\begin{cases}
4.5E,&0\leq E<0.018,\\
1.099E^{0.45}-0.099,&0.018\leq E\leq1.
\end{cases}
$$
The primed components are formed separately before combining them.<Recommendation ITU-R BT.709-6>[Printed page3, item1.1; page4, items3.1–3.2]{ref}
An original calculation shows why the order matters. For a linear red primary $(R,G,B)=(1,0,0)$, the primed triple is also $(1,0,0)$ and luma is 0.2126. Combining the linear channels first gives normalized linear luminance $Y=0.2126$; applying $f$ to that scalar gives approximately 0.4485. Thus
$$
0.2126f(1)+0.7152f(0)+0.0722f(0)
\ne f\bigl(0.2126(1)+0.7152(0)+0.0722(0)\bigr).
$$
Nonlinear encoding does not commute with this channel combination.
In <YCbCr>, luma is stored alongside colour-difference information. <Chroma subsampling> can preserve the luma sampling grid while reducing the other components' sampling. A luma image can therefore retain fine spatial variation without carrying every colour distinction of the original image; it is not a complete colour description.
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