On Mon, Jun 24, 2019 at 8:10 AM Todd <toddr...@gmail.com> wrote:
> On Mon, Jun 24, 2019 at 11:00 AM Stephan Hoyer <sho...@gmail.com> wrote:
>
>> On Sun, Jun 23, 2019 at 10:05 PM Stewart Clelland <
>> stewartclell...@gmail.com> wrote:
>>
>>> Hi All,
>>>
>>> Based on discussion with Marten on github
>>> <https://github.com/numpy/numpy/issues/13797>, I have a couple of
>>> suggestions on syntax improvements on array transpose operations.
>>>
>>> First, introducing a shorthand for the Hermitian Transpose operator. I
>>> thought "A.HT" might be a viable candidate.
>>>
>>
>> I agree that short-hand for the Hermitian transpose would make sense,
>> though I would try to stick with "A.H". It's one of the last reasons to
>> prefer the venerable np.matrix. NumPy arrays already has loads of
>> methods/properties, and this is a case (like @ for matrix multiplication)
>> where the operator significantly improves readability: consider "(x.H @
>> M @ x) / (x.H @ x)" vs "(x.conj().T @ M @ x) / (x.conj().T @ x)" [1].
>> Nearly everyone who does linear algebra with complex numbers would find
>> this useful.
>>
>> If I recall correctly, the last time this came up, it was suggested that
>> we might implement this with NumPy view as a "complex conjugate" dtype
>> rather than a memory copy. This would allow the operation to be essentially
>> free. I find this very appealing, both due to symmetry with ".T" and
>> because of the principle that properties should be cheap to compute.
>>
>> So my tentative vote would be (1) yes, let's do the short-hand attribute,
>> but (2) let's wait until we have a complex conjugate dtype that do this
>> efficiently. My hope is that this should be relatively doable in a year or
>> two after current dtype refactor/usability effect comes to fruition.
>>
>> Best,
>> Stephan
>>
>> [1] I copied the first non-trivial example off the Wikipedia page for a
>> Hermitian matrix: https://en.wikipedia.org/wiki/Hermitian_matrix
>>
>>
> I would call it .CT or something like that, based on the term "Conjugate
> transpose". Wikipedia redirects "Hermitian transpose" to "Conjugate
> transpose", and google has 49,800 results for "Hermitian transpose" vs
> 201,000 for "Conjugate transpose" (both with quotes). So "Conjugate
> transpose" seems to be the more widely-known name. Further, I think what a
> "Conjugate transpose" does is immediately obvious to someone who isn't
> already familiar with the term so long as they know what a "conjugate" and
> "transpose" are, while no one would be able to tell what a "Hermitian
> transpose" unless they are already familiar with the name. So I have no
> problem calling it a "Hermitian transpose" somewhere in the docs, but I
> think the naming and documentation should focus on the "Conjugate
> transpose" term.
>
Sure, we should absolutely document the name as the "Conjugate transpose".
But the standard mathematical notation is definitely "A^H" rather than
"A^{CT}".
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