HilbertSpace concept
Description
A Hilbert space is a combination of
PseudoHilbertSpace
, equipped with
BanachSpace
, where the norm is induced from the inner product as
||x|| = <x,x>
1/2
.
Refinement of
PseudoHilbertSpace
.
BanachSpace
.
Associated types
Those defined by
PseudoHilbertSpace
and
BanachSpace
:
Notation
X
A type that is a model of HilbertSpace
v,w
Object of type
X
Definitions
Valid expressions
Those defined by
PseudoHilbertSpace
and
BanachSpace
.
Expression semantics
Complexity guarantees
Invariants
v.norm() = inner_prod( v, v )
1/2
;
Models
euclidean_space
<
vector
>.
Notes