Noun
Euclidean distance (countable and uncountable, plural Euclidean distances)
(geometry) The distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points; for example, in two-dimensional Euclidean geometry, the Euclidean distance between two points a = (ax, ay) and b = (bx, by) is defined as:
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{\displaystyle d({\textbf {a}},{\textbf {b}})={\sqrt {({\textbf {a}}_{x}-{\textbf {b}}_{x})^{2}+({\textbf {a}}_{y}-{\textbf {b}}_{y})^{2}}}}
Nevertheless, an obvious upper bound to the rate is related to the minimum Euclidean distance of the constellation (the shortest straight-line distance between two points): : Again, the bit-error rate will depend on the assignment of bits to symbols. Source: Internet
Why is Euclidean distance not a good metric in high dimensions? Source: Internet
Definition The Euclidean distance between points p and q is the length of the line segment connecting them ( ). Source: Internet
If we consider that its length is actually the distance from its tail to its tip, it becomes clear that the Euclidean norm of a vector is just a special case of Euclidean distance: the Euclidean distance between its tail and its tip. Source: Internet
In fact, a "metric" is the generalization of the Euclidean metric arising from the four long-known properties of the Euclidean distance. Source: Internet
The circular 8-QAM constellation is known to be the optimal 8-QAM constellation in the sense of requiring the least mean power for a given minimum Euclidean distance. Source: Internet