leanprover-community / leanprover-community/mathlib4
Feature Request: Schur complement for block matrices and singular value bounds
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Description
Matrix.schur_complement As a defined object with M/A = D - C A⁻¹ B
need it: formal verification of power system stability bounds
What exists: Matrix.PosSemidef is there, Schur decomposition is there, complement is missing
Contributor guide
First steps
- Read the whole issue, then the project's contributing guide.
- Comment on the issue to say you are picking it up — it saves two people doing the same work.
- Fork the repository and make your change on a branch.
- Open a pull request that references the issue number.
Research direction
Start by reading Matrix.PosSemidef and the existing Schur decomposition, then trace how matrix-defined objects are represented and tested. Define the intended Matrix.schur_complement object using M/A = D - C A⁻¹ B, and clarify whether the singular-value bounds are part of the same change before considering the work complete.
Written by the indexing model from the issue text.
Assessment
- Domain
- tooling
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Quiet
- Clarity
- Mostly clear
- Newbie friendliness
- 45/100