Quantum / CONCEPT
A counterexample to strict spectral convergence
Schatten-p approximants need not converge to the strict spectral approximant. A complex linear subspace of three-by-three matrices has a strict residual with singular values (1,1,0), whereas every minimizing residual for sufficiently large p has real last diagonal entry less than -1/4.
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DIRECT PREREQUISITES4
DIRECT CONSEQUENCES1
PROOF DEPTH7
DOCUMENT LINKS0
Real powers of a square
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Direct recorded relationships
Proof dependencyStructural affinityDocument link
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Certified topology / DOWNSTREAM
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RELATED KNOWLEDGE
Structural connections
- A counterexample to the Young-subgroup cross-sum inequalitystructural-affinity · Closed
- Factorial Partition Signs: Conjecture 4.4 is Falsestructural-affinity · Closed
- Finite two-row trace powerstructural-affinity · Closed
- Noninteger parameters do not ensure injectivity on integer partitionsstructural-affinity · Closed
- OccupationPartialTransposeSpectralstructural-affinity · Closed
- Path and Spectral Forms of the Log-Determinant Divergencestructural-affinity · Closed
- QuditPartialEstimationTradeoffstructural-affinity · Closed
- Shared Schatten continuitystructural-affinity · Closed
- The modified Bessel product need not be log-convex in its orderstructural-affinity · Closed
- Two eigenvalue chart and boundary regularizationstructural-affinity · Closed
- Upper norm compression reduces to three block columnsstructural-affinity · Closed
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