Week of 1/21/08

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Revision as of 15:35, 21 January 2008

$\langle u+v,w \rangle \equiv \langle u,w \rangle + \langle v,w \rangle$

$\langle u,v+w \rangle \equiv \langle u,v \rangle + \langle u,w \rangle$

$\langle \alpha u,v \rangle \equiv \alpha \langle u,v \rangle$

$\langle u,\alpha v \rangle \equiv \alpha^* \langle u,v \rangle$

$\langle u,v \rangle \equiv \langle v,u \rangle ^*$

$\langle u,u \rangle = 0,$ with equality only if $u = = 0$

The basic example is the form

$h(z,w) \equiv \sum z_i w^* _i$

@@ Line 3: / Line 3: @@
 <math> \langle u+v,w \rangle \equiv \langle u,w \rangle + \langle v,w \rangle </math>
-<math> \langle u,v+w \rangle  \equiv langle u,v \rangle + \langle u,w \rangle </math>
+<math> \langle u,v+w \rangle  \equiv \langle u,v \rangle + \langle u,w \rangle </math>
 <math> \langle \alpha u,v \rangle  \equiv \alpha \langle u,v \rangle </math>