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Add Cholesky decomposition implementation #13982

@markonnn

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@markonnn

Feature description

Proposal: Add an implementation of the Cholesky factorization for symmetric, positive-definite matrices within the linear_algebra module.

The module currently lacks a Cholesky factorization. Introducing this implemntation will make the underlying algorithmic steps explicit and enhance educational clarity.

My plan:

  • Implement cholesky_decomposition(A) -> L
  • Implement cholesky_solve(A, b) using forward/back substitution
  • Add full docstrings with doctests
  • Add pytest tests in the test directory
  • Include validation for symmetry and positive-definiteness where appropriate
  • Follow the folder structure and style of the existing algorithms

Please indicate whether this contribution is appropriate or if there are any specific guidelines I should follow.

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