Kernels, images and projections in dioids. G. Cohen, S. Gaubert, J.P. Quadrat. Proceedings of WODES' 96. Edinburgh, Scotland, UK, 19-21 August, 1996.

We consider the projection problem for linear spaces and operators over dioids such as the $(\max,+)$ semiring. We give existence and uniqueness conditions for the projection onto the image of an operator, parallel to the kernel of another one, together with an explicit formula for the projector. The theory is not limited to linear operators: the result holds more generally for residuated operators over complete dioids. Illustrative examples are provided.