Zeros / CONCEPT
Schur–Frobenius inequality and equality
The squared moduli of a complex matrix's eigenvalues sum to at most its squared Frobenius norm, with equality exactly for normal matrices.
Closed
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES1
PROOF DEPTH8
DOCUMENT LINKS0
Eigenvalue energy and matrix energy
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
- A positive map reflecting positive contractionsstructural-affinity · Closed
- An explicit rate for the fixed controlstructural-affinity · Closed
- Cartesian variancestructural-affinity · Closed
- Commutator gap and scalar translationstructural-affinity · Closed
- Equal Gram Unitary Extensionstructural-affinity · Closed
- Radial convexity and endpoint derivativesstructural-affinity · Closed
- Tang–Zhang's real-order reciprocal critical-point inequalitystructural-affinity · Closed
- Tang–Zhang's sharp order −2 inequalitystructural-affinity · Closed
- The most classical orthonormal basis of spin 3/2structural-affinity · Closed
- The original two-swap channelstructural-affinity · Closed
- The sharp spectral moment inequalitystructural-affinity · Closed
- Trace bounds, interpolation and phase rigiditystructural-affinity · Closed
- Weak products do not preserve edge-complexity equalitystructural-affinity · Closed
- Weighted Bottcher-Wenzel, case (ii)structural-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
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