Quantum / CONCEPT
A counterexample to mixed-power norm monotonicity
Two positive definite rational matrices reverse the trace-norm comparison at powers one half and three quarters, refuting the proposed monotonicity for all unitarily invariant norms.
Closed
DIRECT PREREQUISITES3
DIRECT CONSEQUENCES0
PROOF DEPTH6
DOCUMENT LINKS0
Conjecture 1 is false
RELATIONSHIP ATLAS
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Direct recorded relationships
Proof dependencyStructural affinityDocument link
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Prerequisites
Certified topology / DOWNSTREAM
Consequences
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RELATED KNOWLEDGE
Structural connections
- A positive block does not force normalitystructural-affinity · Closed
- Classical finite mixturesstructural-affinity · Closed
- Coherent Premeasurement and Correlation Taxstructural-affinity · Closed
- Entropy Production by Coherence Deletionstructural-affinity · Closed
- Fuchs's physical-basis logarithm question is falsestructural-affinity · Closed
- Spectral powers and matrix positivitystructural-affinity · Closed
- The trace norm and its two-dimensional formulastructural-affinity · Closed
- Word traces do not control fractional Schatten normsstructural-affinity · Closed
Documents & exposition
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