feat(LinearAlgebra/BilinearForm): add indefinite metrics#38194
feat(LinearAlgebra/BilinearForm): add indefinite metrics#38194ryanncode wants to merge 1 commit intoleanprover-community:masterfrom
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Add the `IndefiniteMetric` structure to support vector spaces equipped with a non-degenerate, symmetric, indefinite bilinear form. Provide the algebraic foundation for indefinite inner product spaces by formalizing the metric via `LinearMap.BilinForm` and extracting its associated quadratic form without enforcing the `IsPosSemidef` typeclass. Previously, mathlib required strictly positive-definite metrics to instantiate inner product spaces (`InnerProductSpace`), which prevented the formalization of indefinite geometries without causing typeclass inference failures. Bridge this gap by isolating the symmetric bilinear form from topological and positivity constraints, allowing the library to handle generalized indefinite metric spaces safely.
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PR summary 9036ce5439Import changes for modified filesNo significant changes to the import graph Import changes for all files
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Add the
IndefiniteMetricstructure to support vector spaces equipped with a non-degenerate, symmetric, indefinite bilinear form.Provide the algebraic foundation for indefinite inner product spaces by formalizing the metric via
LinearMap.BilinFormand extracting its associated quadratic form without enforcing theIsPosSemideftypeclass.Previously, mathlib required strictly positive-definite metrics to instantiate inner product spaces (
InnerProductSpace), which prevented the formalization of indefinite geometries without causing typeclass inference failures. Bridge this gap by isolating the symmetric bilinear form from topological and positivity constraints, allowing the library to handle generalized indefinite metric spaces safely.