Quantum / CONCEPT
A counterexample to the radial convexity characterization
Radial convexity with respect to the Frobenius norm does not imply matrix monotonicity of the same degree: an explicit rational function separates the two properties in degree three.
Closed
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES0
PROOF DEPTH10
DOCUMENT LINKS0
Opposite signs on an ordered positive pair
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
None recorded in this release.
RELATED KNOWLEDGE
Structural connections
- A three-node resolvent estimatestructural-affinity · Closed
- Cartesian variancestructural-affinity · Closed
- Commutator gap and scalar translationstructural-affinity · Closed
- Entropy under entrywise modulus in dimension threestructural-affinity · Closed
- Positivity at both endpointsstructural-affinity · Closed
- Radial convexity and endpoint derivativesstructural-affinity · Closed
- Resolvent derivatives and radial distancestructural-affinity · Closed
- The rational functional-calculus expressionstructural-affinity · Closed
- Zero diagonal blocksstructural-affinity · Closed
Documents & exposition
None recorded in this release.
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
Loading release versions...
Browse the archiveCertified provenance