Personal authentication using electroencephalographic (EEG) signals, is one of the important applications in brain computer interface (BCI). In this work we investigate the use of EEG signals as a biometric trait. Multidimensional EEG signals were represented as symmetric positive-definite (SPD) matrices on a Riemannian manifold. Two experiments are performed in the first; we use minimum distance to Riemannian mean (MDRM) as a classifier. In the second; SPD matrices are vectorized, and the generated vectors are used to train various machine learning (ML) classifiers. MDRM classifier achieved a correct recognition rate (CRR) of 96.92% , while ML classifiers achieved CRR from 95.39% to 99.45%.