Matrix Factorizations for LinearOperators

[marvinpfoertner]

Is your feature request related to a problem? Please describe.
Currently, the implementation of Normal contains a lot of logic concerning the efficient computation of Cholesky factorizations of LinearOperators with Kronecker and SymmetricKronecker structure.
This adds unnecessary complexity and is out of place in the implementation of a RandomVariable.
We should add a cholesky method to the LinearOperator, which then takes care of the specific factorizations in its subclasses.

Give an example use case.

>>> A = pn.linops.Kronecker(A=..., B=...)
>>> L = A.cholesky(lower=True)
>>> type(L)
pn.linops.Kronecker
>>> x = A.inv() @ b  # uses Cholesky internally!

Describe the solution you'd like.

• LinearOperator.cholesky(lower: bool = True)
  • Matrix properties is_symmetric, is_positive_definite, is_{lower,upper}_triangular, see Matrix Property System for LinearOperators #571
  • InverseLinearOperator should use cholesky if linop.symmetric and linop.positive_definite are True
• LinearOperator.pivoted_lu
  • Matrix properties is_{lower,upper}_triangular, is_orthogonal, see Matrix Property System for LinearOperators #571
  • InverseLinearOperator should use LinearOperator.plu
  • LinearOperator.{log}det should use LinearOperator.plu as a fallback
• LinearOperator.svd
  • Matrix property is_orthogonal, see Matrix Property System for LinearOperators #571
  • Compute LinearOperator.eigvals from svd if linop.symmetric are True
  • Compute LinearOperator.eigh from svd if linop.symmetric are True
• LinearOperator.eig
  • Matrix properties is_symmetric, is_orthogonal, see Matrix Property System for LinearOperators #571
• LinearOperator.{qr, lq}
  • Matrix properties is_{lower,upper}_triangular, is_orthogonal, see Matrix Property System for LinearOperators #571
• LinearOperator.{log}det fallback implementation
  • try using linop.cholesky if linop.symmetric is True
  • if this does not work, use linop.pivoted_lu

Additional context
Some of the properties from #571 are needed to implement these factorizations.