Pure Mathematics for Theoretical Computer Science PMTCS 2995-3162 10.54216/PMTCS https://www.americaspg.com/journals/show/2822 2023 2023 Hama University, Department of Mathematics, Hama, Syria Husain Husain In this paper, we prove the following result: If the space  (the finite sequences) is equipped with the norm which is naturally induced by a positive definite Hermitian and diagonally blockwise constructed matrix, then an HK completion exists. Also, we investigate our result through many illustrated examples. 2024 2024 40 43 10.54216/PMTCS.030203 https://www.americaspg.com/articleinfo/40/show/2822