Category:Isometries (Inner Product Spaces)
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This category contains results about isometries in the context of inner product spaces.
Definitions specific to this category can be found in Definitions/Isometries (Inner Product Spaces).
Let $V$ and $W$ be inner product spaces.
Let their inner products be $\innerprod \cdot \cdot_V$ and $\innerprod \cdot \cdot_W$ respectively.
Let the mapping $F : V \to W$ be a vector space isomorphism that preserves inner products:
- $\forall v_1, v_2 \in V : \innerprod {v_1} {v_2}_V = \innerprod {\map F {v_1}} {\map F {v_2}}_W$
Then $F$ is called a (linear) isometry.
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