The Resolvent Average for Positive Semidefinite Matrices

Details The Resolvent Average for Positive Semidefinite Matrices The Resolvent Average for Positive Semidefinite Matrices

2009-10-19

arxiv.org/abs/0910.3705v1

Mathematics

Functional Analysis

Scientific paper

We define a new average - termed the resolvent average - for positive semidefinite matrices. For positive definite matrices, the resolvent average enjoys self-duality and it interpolates between the harmonic and the arithmetic averages, which it approaches when taking appropriate limits. We compare the resolvent average to the geometric mean. Some applications to matrix functions are also given.

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