Modeling visual data onto the SPD (symmetric positive definite) manifold using the SPD matrices has been proven to yield high discriminatory power for many visual classification tasks in the domain of pattern recognition and machine learning. Among them, generalising the sparse representation classification algorithm to the SPD manifold-based visual classification tasks has attracted extensive attention. This study first comprehensively reviews the characteristics of the sparse representation classification algorithm and the Riemannian geometrical structure of the SPD manifold. Then, embedding the SPD manifold into the Reproducing Kernel Hilbert Space (RKHS) via a kernel function. Afterwards, the latent sparse representation model and latent classification model in RKHS has been suggested, respectively. However, the original visual data in RKHS is implicitly described, which is impossible to perform the subsequent dictionary learning. To handle this issue, the Nyström method is utilized to obtain the approximate representations of the training samples in RKHS for the sake of updating the latent dictionary and latent matrix. Finally, the classification results obtained on five benchmarking datasets show the effectiveness of the proposed approach.