Pre-Hilbert space
Set
| context | V |
| definiendum | ⟨V,⟨⋅|⋅⟩⟩∈PreHilbert(V) |
| context | V∈VectorSpace(V,C) |
| context | ⟨⋅|⋅⟩:V×V→C |
| u,v,w∈V |
| a,b∈C |
| postulate | ¯⟨v|w⟩=⟨w|v⟩ |
| postulate | v≠0⇒⟨v|v⟩>0 |
| postulate | v=0⇒⟨v|v⟩=0 |
| postulate | ⟨u|a⋅v+b⋅w⟩=a⋅⟨u|v⟩+b⋅⟨u|w⟩ |
| postulate | ⟨a⋅v+b⋅w|u⟩=¯a⋅⟨v|u⟩+¯b⋅⟨w|u⟩ |
Discussion
Reference
Wikipedia: Inner product space
Parents
Refinement of
Context
