Von Neumann's trace inequality
Encyclopedia
In mathematics, von Neumann's trace inequality, named after its originator John von Neumann
, states that for any n × n complex matrices A, B with singular values
and 
respectively,
(See Trace (linear algebra)
.)
John von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...
, states that for any n × n complex matrices A, B with singular values
and respectively,(See Trace (linear algebra)
Trace (linear algebra)
In linear algebra, the trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal of A, i.e.,...
.)
External links
- Darren Rhea, von Neumann's Trace Inequality (pdf proof)