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orthonormal_basis [2013/09/01 00:12] nikolaj |
orthonormal_basis [2014/03/21 11:11] (current) |
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| ===== Orthonormal basis ===== | ===== Orthonormal basis ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $V$...pre-Hilbert space | | + | | @#55CCEE: context | @#55CCEE: $V$...pre-Hilbert space | |
| - | | @#FFBB00: $B\in \mathrm{OrthonormalBasis}(V)$ | | + | | @#FFBB00: definiendum | @#FFBB00: $B\in \mathrm{OrthonormalBasis}(V)$ | |
| - | | @#88DDEE: $B\in \mathrm{Basis}(V)$ | | + | | @#55CCEE: context | @#55CCEE: $B\in \mathrm{Basis}(V)$ | |
| | $v,w\in B$ | | | $v,w\in B$ | | ||
| - | | @#55EE55: $v\ne w\implies \langle v|w\rangle = 0 $ | | + | | @#55EE55: postulate | @#55EE55: $v\ne w\implies \langle v|w\rangle = 0 $ | |
| - | | @#55EE55: $\Vert v\Vert = 1 $ | | + | | @#55EE55: postulate | @#55EE55: $\Vert v\Vert = 1 $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| - | ==== Context ==== | + | ==== Parents ==== |
| === Subset of === | === Subset of === | ||
| [[Orthogonal basis]] | [[Orthogonal basis]] | ||
