We outline how a specific product with a symmetric matrix representation is complemented by a suitable antisymmetric product such that the sum of these matrix products yields a real-number matrix representation of the geometric product for the case of vectors in three-dimensional space. To the best of the authors' knowledge, this direct correspondence of 'abstract' geometric algebra with 'concrete' matrix algebra has not been documented yet. At first the basic observation may be useful for practical computations, at least it opens a door for further research. Finally, the connection underlines the relevance of geometric calculus as a powerful tool for various fields of research and engineering.