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.

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