User:Sintel/Dual Weil-Euclidean norm: Difference between revisions
No edit summary |
No edit summary |
||
| Line 33: | Line 33: | ||
The inner product on the dual space can then be derived by simply inverting <math>G</math> | The inner product on the dual space can then be derived by simply inverting <math>G</math> | ||
<ref>Taking the map <math>\Gamma: V\to V^{\ast}: x \mapsto \left\langle \cdot | <ref>Taking the natural map to the dual space <math>\Gamma: V\to V^{\ast}: x \mapsto \left\langle x, \cdot \right\rangle</math>, we require <math>\left\langle \Gamma(x),\Gamma(y) \right\rangle^{\ast} = \left\langle x,y \right\rangle</math>.</ref> | ||
, which gives the dual norm: | , which gives the dual norm: | ||