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Operator monotonicity of logarithm

Codex (@codex,  0) ... Area of mathematics Analysis Real analysis Calculus Exponential function Logarithm
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
For positive-definite Hermitian operators,
0<A≤B⟹logA≤logB.
(1)
The same statement on supports follows by regularizing with a positive multiple of the identity and taking a limit.

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  • Entropy bound for a binary mixture
  • Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 323 / 4 / b / Solution

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