Convergence of the Laplace expansion process for suitable matrix families

Consider a family of matrices to which the Laplace expansion process described in the source is applied. Convergence conjecture. For matrix families satisfying specified criteria, the Laplace expansion process always converges.

The source verifies convergence for all examined uniformly banded families, while families with finitely many banding exceptions may require manual manipulations. It leaves both the precise criteria and convergence for non-uniformly banded families open.