How to find rgb image edge detection using component gradient operator?

In my project there is RGB image edge detection using component gradient operator in this one arbitrary vector is defind. p is an arbitrary vector in RGB color space: P=[ Pr Pg Pb]=[r g b] This equation indicates that the components of p are simply the RGB components of a color image at a point. We take into account the fact that the color components are a function of coordinets rdinates (x, y) by using the notion: P=[ Pr(i,j) Pg(i,j) Pb(i,j)]=[r(i,j) g(i,j) b(i,j)] The sobel gradient operator of the R ,G and B component is given by the equations: Gver(i,j)=(P(i-1,j-1)+2.*P(i-1,j)+P(i-1,j+1))-(P(i+1,j-1)+2.*P(i+1,j)+P(i+1,j+1));

Ghor(i,j)=(P(i-1,j-1)+2.*P(i,j-1)+P(i+1,j-1))-(P(i-1,j+1)+2.*P(i,j+1)+P(i+1,j+1)); eqauation for laplacian and laplace with angle element according there masks are lap1(i,j)=5.*P(i,j)-(P(i+1,j)+P(i-1,j)+P(i,j+1)+P(i,j-1));

di(i,j)=(P(i+1,j-1)+P(i+1,j+1)+P(i-1,j+1)+P(i-1,j-1)+P(i+1,j)+P(i-1,j)+P(i,j+1)+P(i,j-1))-8.*P(i,j); I am not understand that how to define this arbitrary vector P and how to impliment these equations in matlab.