On the Existence of Kernel Function for Kernel-Trick of k-Means

This paper corrects the proof of the Theorem 2 from the Gower's paper \cite[page 5]{Gower:1982}. The correction is needed in order to establish the existence of the kernel function used commonly in the kernel trick e.g. for $k$-means clustering algorithm, on the grounds of distance matrix. The scope of correction is explained in section 2.