  This paper corrects the proof of the Theorem 2 from the Gower's paper
\cite[page 5]{Gower:1982} as well as corrects the Theorem 7 from Gower's paper
\cite{Gower:1986}. The first 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
correction encompasses the missing if-part proof and dropping unnecessary
conditions. The second correction deals with transformation of the kernel
matrix into a one embeddable in Euclidean space.
