The prevalent way to estimate the similarity of two documents based on word embeddings is to apply the cosine similarity measure to the two centroids obtained from the embedding vectors associated with the words in each document. Motivated by an industrial application from the domain of youth marketing, where this approach produced only mediocre results, we propose an alternative way of combining the word vectors using matrix norms. The evaluation shows superior results for most of the investigated matrix norms in comparison to both the classical cosine measure and several other document similarity estimates.