Now that we know how to create a 3×3 linear matrix to convert white balanced and demosaiced raw data into 
connection space – and where to obtain the 3×3 linear matrix to then convert it to a standard output color space like sRGB – we can take a closer look at the matrices and apply them to a real world capture chosen for its wide range of chromaticities.
We understand from the previous article that rendering color with Adobe DNG raw conversion essentially means mapping raw data in the form of 
triplets into a standard color space via a Profile Connection Space in a two step process
![\[ Raw Data \rightarrow XYZ_{D50} \rightarrow RGB_{standard} \]](https://i0.wp.com/www.strollswithmydog.com/wordpress/wp-content/ql-cache/quicklatex.com-062c1798a46be7f6f42a79b450d40bde_l3.png?resize=298%2C15&ssl=1 "Rendered by QuickLaTeX.com")
The first step white balances and demosaics the raw data, which at that stage we will refer to as , followed by converting it to Profile Connection Space through linear projection by an unknown ‘Forward Matrix’ (as DNG calls it) of the form
(1) ![\begin{equation*} \left[ \begin{array}{c} X_{D50} \\ Y_{D50} \\ Z_{D50} \end{array} \right] = \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{bmatrix} \left[ \begin{array}{c} r \\ g \\ b \end{array} \right] \end{equation*}](https://i0.wp.com/www.strollswithmydog.com/wordpress/wp-content/ql-cache/quicklatex.com-b9f4277814179e1fbcf64e1a69a53818_l3.png?resize=273%2C64&ssl=1 "Rendered by QuickLaTeX.com")
with data as column-vectors in a 3xN array. Determining the nine 
coefficients of this matrix 
is the main subject of this article[1]. Continue reading Color: Determining a Forward Matrix for Your Camera