The Collaborative Representation (CR) framework has provided various effective and efficient solutions to pattern analysis. By leveraging between discriminative coefficient coding (l 2 regularization) and the best reconstruction quality (collaboration), the CR framework can exploit discriminative patterns efficiently in high-dimensional space. Due to the limitations of its linear representation mechanism, the CR must sacrifice its superior efficiency for capturing the non-linear information with the kernel trick. Besides this, even if the coding is indispensable, there is no mechanism designed to keep the CR free from inevitable noise brought by real-world information systems. In addition, the CR only emphasizes exploiting discriminative patterns on coefficients rather than on the reconstruction. To tackle the problems of primitive CR with a unified framework, in this article we propose the Euler Collaborative Representation (E-CR) framework. Inferred from the Euler formula, in the proposed method, we map the samples to a complex space to capture discriminative and non-linear information without the high-dimensional hidden kernel space. Based on the proposed E-CR framework, we form two specific classifiers: the Euler Collaborative Representation based Classifier (E-CRC) and the Euler Probabilistic Collaborative Representation based Classifier (E-PROCRC). Furthermore, we specifically designed a robust algorithm for E-CR (termed as R-E-CR ) to deal with the inevitable noises in real-world systems. Robust iterative algorithms have been specially designed for solving E-CRC and E-PROCRC. We correspondingly present a series of theoretical proofs to ensure the completeness of the theory for the proposed robust algorithms. We evaluated E-CR and R-E-CR with various experiments to show its competitive performance and efficiency.