<P> For each vector p = (p, p, p, 1) we would have </P> <Dl> <Dd> S v p = (1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 s) (p x p y p z 1) = (p x p y p z 1 s) (\ displaystyle S_ (v) p = (\ begin (bmatrix) 1&0&0&0 \ \ 0&1&0&0 \ \ 0&0&1&0 \ \ 0&0&0& (\ frac (1) (s)) \ end (bmatrix)) (\ begin (bmatrix) p_ (x) \ \ p_ (y) \ \ p_ (z) \ \ 1 \ end (bmatrix)) = (\ begin (bmatrix) p_ (x) \ \ p_ (y) \ \ p_ (z) \ \ (\ frac (1) (s)) \ end (bmatrix))) </Dd> </Dl> <Dd> S v p = (1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 s) (p x p y p z 1) = (p x p y p z 1 s) (\ displaystyle S_ (v) p = (\ begin (bmatrix) 1&0&0&0 \ \ 0&1&0&0 \ \ 0&0&1&0 \ \ 0&0&0& (\ frac (1) (s)) \ end (bmatrix)) (\ begin (bmatrix) p_ (x) \ \ p_ (y) \ \ p_ (z) \ \ 1 \ end (bmatrix)) = (\ begin (bmatrix) p_ (x) \ \ p_ (y) \ \ p_ (z) \ \ (\ frac (1) (s)) \ end (bmatrix))) </Dd> <P> which would be homogenized to </P>

2d and 3d coordinate system in computer graphics