trureturingGitHub MATHEMATICAL ATLAS

QuadraticForms / CONCEPT

Structured rank-one inertia

Structured downdates of real symmetric matrices have exact positive, negative and zero eigenvalue counts, including singular forms.

Closed Authored exposition
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES2
PROOF DEPTH6
DOCUMENT LINKS0
THEOREM

Real diagonal sign counts

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Direct recorded relationships
Point-Gap Exact InertiaPoint-Gap Exact InertiaInvertible Hermitian Inertia PullbackInvertible Hermitian InertiaPullbackStructured rank-one inertiaStructured rank-one inertiaSingular multipartite squared-distance LaplacianSingular multipartite squared-distance LaplacianContinuous structured downdates on the original domainContinuous structured downdateson the original domain
Proof dependencyStructural affinityDocument link

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Structural connections

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Certified provenance

Exact release coordinate

Lean sourceResearch workspace
Status
Closed
Depth
6
Layer
D5/S3
Domain
QuadraticForms
Node ID
D5/S3/QuadraticForms/StructuredRankOneInertia
Repository path
D5/S3/QuadraticForms/StructuredRankOneInertia.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
Source tree
37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

Authority boundary

Dependency edges, status, and source coordinates come from the verified release and certified topology. Blueprint exposition is labeled separately. A fallback title carries no additional mathematical authority.