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feat(LinearAlgebra/Matrix/Charpoly): general coefficient formula as sum of principal minors#37625

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feat(LinearAlgebra/Matrix/Charpoly): general coefficient formula as sum of principal minors#37625
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slavanaprienko:feat-charpoly-coeff-minors

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@slavanaprienko slavanaprienko commented Apr 3, 2026

This PR adds a general formula for the coefficients of det(1 + X • M) as sums of principal minors, generalizing the existing coeff_det_one_add_X_smul_one (k=1, trace) and det_eq_sign_charpoly_coeff (k=n, determinant). It also derives the corresponding formula for the coefficients of the characteristic polynomial via charpolyRev.

New results:

  • det_piecewise_one_eq_submatrix_det: relates piecewise-with-identity to principal submatrix determinants
  • coeff_det_one_add_X_smul_eq_sum_minors: the k-th coefficient of det(1 + X • M) equals the sum of k×k principal minors
  • charpoly_coeff_eq_sum_minors: coefficients of the characteristic polynomial as signed sums of principal minors

@github-actions github-actions bot added the new-contributor This PR was made by a contributor with at most 5 merged PRs. Welcome to the community! label Apr 3, 2026
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github-actions bot commented Apr 3, 2026

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github-actions bot commented Apr 3, 2026 •
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PR summary 290b6cf8be

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ charpoly_coeff_eq_sum_minors
+ coeff_det_one_add_X_smul_eq_sum_minors
+ det_piecewise_one_eq_submatrix_det

You can run this locally as follows 
## summary with just the declaration names:
./scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.

No changes to technical debt.

You can run this locally as

./scripts/reporting/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

@github-actions github-actions bot added the t-algebra Algebra (groups, rings, fields, etc) label Apr 3, 2026
eric-wieser
eric-wieser reviewed Apr 4, 2026
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eric-wieser
eric-wieser reviewed Apr 4, 2026
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