Arith / CONCEPT
Hadamard Bound for Integer Matrices
A positive definite integer matrix has a positive integer determinant bounded by its diagonal product, with equality exactly for a diagonal matrix.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES2
PROOF DEPTH3
DOCUMENT LINKS1
Positive integer determinant and equality condition
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- Catalan Difference Moment Ratiosstructural-affinity · Closed
- Congruence Geometry of the Log-Determinant Divergencestructural-affinity · Closed
- Discrete Logarithmic Selectorstructural-affinity · Closed
- Equality in the Log-Determinant Divergencestructural-affinity · Closed
- Integer Fischer Selectorstructural-affinity · Closed
- Nonnegativity of the Log-Determinant Divergencestructural-affinity · Closed
- Pythagorean Projection Certificates for Log-Det Divergencestructural-affinity · Closed
- Squared-Catalan Hankel Growthstructural-affinity · Closed
- Squared-Catalan Hankel Limitsstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
Loading release versions...
Browse the archiveCertified provenance