Fix matrix-matrix hadamard power

[sylee957]

References to other Issues or PRs

Fixes #16505

Brief description of what is fixed or changed

If both base and exponent are matrix, hadamard power can be defined from hadamard exponential and logarithm as usual definition for the matrix power.

And since hadamard exponential and hadamard log are elementwise exponential and logarithm, it can be reduced to

for each matrix elements.

Still the definition for the hadamard power between a matrix and a scalar is unclear, however, if it is defined as usual matrix-scalar product, it can easily be reduced to the elementwise power.

Other comments

Release Notes

• matrices
  • HadamardProduct.as_explicit now supports matrix to matrix power.
  • Added missing doc for HadamardProduct and HadamardPower.

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• matrices

  • HadamardProduct.as_explicit now supports matrix to matrix power. (#16508 by @sylee957)

  • Added missing doc for HadamardProduct and HadamardPower. (#16508 by @sylee957)

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Fixes #16505

#### Brief description of what is fixed or changed

If both base and exponent are matrix, hadamard power can be defined from hadamard exponential and logarithm as usual definition for the matrix power. 
![image](https://user-images.githubusercontent.com/34944973/63642286-eb650a00-c6f7-11e9-87d2-96f4e7922cb9.png)


And since hadamard exponential and hadamard log are elementwise exponential and logarithm, it can be reduced to
![image](https://user-images.githubusercontent.com/34944973/55284069-53fac580-53aa-11e9-9560-cdc6ebdd1579.png)
for each matrix elements.

Still the definition for the hadamard power between a matrix and a scalar is unclear, however, if it is defined as usual matrix-scalar product, it can easily be reduced to the elementwise power.

#### Other comments


#### Release Notes

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<!-- BEGIN RELEASE NOTES -->
- matrices
  - `HadamardProduct.as_explicit` now supports matrix to matrix power.
  - Added missing doc for `HadamardProduct` and `HadamardPower`.
<!-- END RELEASE NOTES -->

Update

The release notes on the wiki have been updated.

[codecov]

Codecov Report

Merging #16508 into master will decrease coverage by 0.004%.
The diff coverage is 70%.

@@              Coverage Diff              @@
##            master    #16508       +/-   ##
=============================================
- Coverage   74.699%   74.694%   -0.005%     
=============================================
  Files          633       633               
  Lines       164460    164487       +27     
  Branches     38611     38623       +12     
=============================================
+ Hits        122850    122863       +13     
- Misses       36219     36223        +4     
- Partials      5391      5401       +10

[sylee957]

I see sympy raises error when hadamard product between matrix and scalar.
I'm not very clear that hadamard power can be defined with scalar base if it is that way,
Neither am I clear about hadamard power can be defined in this way, because I cannot understand if hadamard exponential is possible (With using taylor series expansion with hadamard product, like as in ordianry matrix exponential is defined), but no scalar-to-matrix power is possible.

We may need some other source to verify

[oscarbenjamin]

This has merge conflicts now...

[sylee957]

Whatever, I couldn't find any good article for the hadamard product notation to be defined between a matrix and scalar, or the hadamard power notation to be defined between a matrix and a matrix, but at least having an option to raise a matrix base to a matrix exponent can be convenient if defined.

If other properties related to the hadamard product or hadamard power do not break with such new definition,
I would define a hadamard product between a matrix and a scalar as a usual matrix-scalar multiplication, and
hadamard power between matrices as entrywise power between each matrix elements, as used in most of the numeric libraries, unless some other people can tackle in.

[sylee957]

I've got the sphinx render, but just wonder why \hdots are showing like that, while the same LaTeX works for https://www.codecogs.com/latex/eqneditor.php And horizontal dots are fixed after changing \hdots to \cdots

[oscarbenjamin]

Looks good. Merging