The difficulty of managing airspace is reflected in the complexity of forecasting its evolution. This paper presents a new neural network framework for managing images for which pixels are matrices with application to air traffic complexity map prediction. By modelling air traffic with a linear dynamical system, air traffic maps can be defined as images whose pixels are matrices. By computing intermediate steps, these air traffic maps are defined as images whose pixels are symmetric positive definite matrices. Then, we implement a convolution neural network with a specific data preprocessing step, new convolution, max-pooling, and flatten layers suitable to such images. The new convolution, max-pooling and flatten layers are capable of processing images coming from the data preprocessing step.