How does Euclidean-norm in K-means cause it to have linear decision boundaries? The Euclidean-norm is a non-linear measure between two points, then how does it make the boundaries till linear?
K-means clustering works by creating a Voronoi diagram that has linear decision boundaries between clusters, as you know. This means that you can draw lines/planes/hyperplanes to classify your data.
In practice, you are actually using the squared euclidean distance because the sum of squares is being minimised by K-means. Because the square root is monotone, this means that the euclidean distance is minimised as well.