Opened 2 years ago
Last modified 6 months ago
#30218 new enhancement
Category InnerProductSpaces
Reported by: | mkoeppe | Owned by: | |
---|---|---|---|
Priority: | major | Milestone: | sage-9.7 |
Component: | linear algebra | Keywords: | |
Cc: | tscrim, mjo, egourgoulhon, gh-mjungmath, kcrisman | Merged in: | |
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
(follow-up from #30092)
We define a category InnerProductSpaces
with element methods inner_product
.
A complication for complex vector spaces: FreeModule
defines:
dot_product
- which ignoresinner_product_matrix
and does not conjugatehermitian_inner_product
- which ignoresinner_product_matrix
but conjugates the left factor (self
)inner_product
- which usesinner_product_matrix
but does not conjugate.
Perhaps we need to add an extra parameter inner_product_hermitian
to FreeModule
. For a complex base ring, the module would only be added to the category of InnerProductSpaces
if this is True
.
MatrixSpace
elements currently do not have inner_product
.
References:
- #10683 ... where
hermitian_inner_product
was introduced - numpy.inner and numpy.dot, numpy.tensordot, numpy.einsum do not conjugate.
- numpy.vdot conjugates the left factor; and also handles the inner product of matrices in the same way.
- SymPy's Matrix.dot has parameters
hermitian
andconjugate_convention
that control if and how factors are conjugated.
Change History (10)
comment:1 Changed 2 years ago by
- Description modified (diff)
comment:2 Changed 2 years ago by
- Milestone changed from sage-9.2 to sage-9.3
comment:3 Changed 18 months ago by
- Milestone changed from sage-9.3 to sage-9.4
comment:4 Changed 18 months ago by
- Cc mjo added
comment:5 follow-up: ↓ 8 Changed 18 months ago by
comment:6 Changed 14 months ago by
- Cc egourgoulhon gh-mjungmath kcrisman added
- Description modified (diff)
comment:7 Changed 13 months ago by
- Milestone changed from sage-9.4 to sage-9.5
comment:8 in reply to: ↑ 5 Changed 12 months ago by
comment:9 Changed 8 months ago by
- Milestone changed from sage-9.5 to sage-9.6
comment:10 Changed 6 months ago by
- Milestone changed from sage-9.6 to sage-9.7
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