Euclidean metric
Noun
Meaning
Euclidean metric (plural Euclidean metrics)
(mathematical analysis) In the space
R
n
{\displaystyle \mathbb {R} ^{n}}
, the metric
d
(
x
→
,
y
→
)
=
(
x
1
−
y
1
)
2
+
(
x
2
−
y
2
)
2
+
.
.
.
+
(
x
n
−
y
n
)
2
{\displaystyle d({\vec {x}},{\vec {y}})={\sqrt {(x_{1}-y_{1})^{2}+(x_{2}-y_{2})^{2}+...+(x_{n}-y_{n})^{2}}}}
where
x
→
=
(
x
1
,
.
.
.
,
x
n
)
{\displaystyle {\vec {x}}=(x_{1},...,x_{n})}
and
y
→
=
(
y
1
,
.
.
.
,
y
n
)
{\displaystyle {\vec {y}}=(y_{1},...,y_{n})}
.