[WIP] Rewrite MatrixAlgebraKit factorization definitions

[mtfishman]

Also clean up the code by focusing on using DiagonalArrays.DeltaMatrix instead of FillArrays.Eye.

[codecov]

Codecov Report

❌ Patch coverage is 84.32836% with 21 lines in your changes missing coverage. Please review.
✅ Project coverage is 50.48%. Comparing base (02c7dea) to head (a81c106).

Files with missing lines	Patch %	Lines
src/kroneckerarray.jl	81.39%	16 Missing ⚠️
src/matrixalgebrakit.jl	89.36%	5 Missing ⚠️

❗ There is a different number of reports uploaded between BASE (02c7dea) and HEAD (a81c106). Click for more details.

HEAD has 4 uploads less than BASE

Flag	BASE (02c7dea)	HEAD (a81c106)
docs	2	1
	6	3

Additional details and impacted files

@@             Coverage Diff             @@
##             main      #43       +/-   ##
===========================================
- Coverage   76.23%   50.48%   -25.76%     
===========================================
  Files          13       11        -2     
  Lines         867      822       -45     
===========================================
- Hits          661      415      -246     
- Misses        206      407      +201     

Flag	Coverage Δ
docs	0.00% <0.00%> (ø)

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