## colour coding vector

A displayed colour can be described as a sum of the degree of red, green and blue components it carries. Each colour can hence be written as a vector $\begin{bmatrix} x \\ y \\ z \end{bmatrix} , 0\leq x,y,z \leq 1$ denoting red, green and blue respectively.

If we notice that pure red $\begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}$ tends to be recorded as $\begin{bmatrix} 0.9 \\ 0.1 \\ 0.01 \end{bmatrix}$ due to random errors,

and pure green $\begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix} \mapsto\begin{bmatrix} 0.01 \\ 0.85 \\ 0.001 \end{bmatrix}$

and pure blue $\begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix} \mapsto\begin{bmatrix} 0.2 \\ 0.01 \\ 0.99 \end{bmatrix}$

then we can obtain the cause of distortion due to random errors as the following matrix $\begin{bmatrix} 0.9 & 0.01 & 0.2 \\ 0.1 & 0.85 & 0.01 \\ 0.01 & 0.001 & 0.99 \end{bmatrix}$

and take the inversion to correct the errors.