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Researchers Bound Matrix Logarithms with New Inequalities
Sharp new inequalities refine existing bounds on matrix logarithms, achieving a demonstrably optimal coefficient in tracing directional derivatives. This result extends beyond matrices, applying now to broader classes of operators on infinite dimensional spaces previously unaddressed by these techniques. It improves upon prior work [1, Proposition 2.
A new inequality for positive semidefinite matrices offers an improved bound on a trace involving the directional derivative of a matrix logarithm. It computes this trace with greater precision than before, extending existing inequalities from matrices to more general mathematical objects called positive trace-class A and self-adjoint B within separable Hilbert space. The work establishes a refined mathematical relationship for…
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