Week of 1/21/08
(Difference between revisions)
(New page: [http://mathworld.wolfram.com/HermitianInnerProduct.html Definition of complex (Hermitian) inner product] <math><u+v,w>==<u,w>+<v,w></math> <math><u,v+w>==<u,v>+<u,w></math> <math><\alp...) |
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[http://mathworld.wolfram.com/HermitianInnerProduct.html Definition of complex (Hermitian) inner product] | [http://mathworld.wolfram.com/HermitianInnerProduct.html Definition of complex (Hermitian) inner product] | ||
| − | <math> | + | <math> \langle u+v,w \rangle \equiv <u,w>+<v,w></math> |
| − | <math><u,v+w> | + | <math><u,v+w> \equiv <u,v>+<u,w></math> |
| − | <math><\alpha u,v> | + | <math><\alpha u,v> \equiv \alpha<u,v></math> |
| − | <math><u,\alpha v> | + | <math><u,\alpha v> \equiv \alpha^* <u,v></math> |
| − | <math> <u,v> | + | <math> <u,v> \equiv <v,u> ^* </math> |
| − | <math> <u,u>>=0,</math> with equality only if <math>u==0</math> | + | <math> <u,u>> = 0, </math> with equality only if <math>u==0</math> |
The basic example is the form | The basic example is the form | ||
| − | <math>h(z,w) | + | <math>h(z,w) \equiv \sum z_i w^* _i</math> |
Revision as of 15:32, 21 January 2008
Definition of complex (Hermitian) inner product
< u,u > > = 0, with equality only if u = = 0
The basic example is the form
