Theorem: Euclidean Metric
Let be an inner product space.
The canonical norm can be used to turn into a metric space by defining a metric in the following way:
PROOF
TODO
Definition: Euclidean Metric
The metric is known as the Euclidean metric on .
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Theorem: Euclidean Metric
Let (V,F,+,⋅) be an inner product space.
The canonical norm can be used to turn V into a metric space by defining a metric in the following way:
d(u,v)=def∣∣u−v∣∣PROOF
TODO
Definition: Euclidean Metric
The metric d is known as the Euclidean metric on V.