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orthonormal_basis [2013/09/01 00:11] nikolaj created |
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: $B\in \mathrm{OrthogonallBasis}(V)$ | | + | | @#55CCEE: context | @#55CCEE: $B\in \mathrm{Basis}(V)$ | |
- | | $v\in B$ | | + | | $v,w\in B$ | |
- | | @#55EE55: $\Vert v\Vert = 1 $ | | + | | @#55EE55: postulate | @#55EE55: $v\ne w\implies \langle v|w\rangle = 0 $ | |
+ | | @#55EE55: postulate | @#55EE55: $\Vert v\Vert = 1 $ | | ||
==== Discussion ==== | ==== Discussion ==== | ||
- | ==== Context ==== | + | ==== Parents ==== |
=== Subset of === | === Subset of === | ||
[[Orthogonal basis]] | [[Orthogonal basis]] |