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Sammanfattning

A pair of complex Hermitian matrices A and B of the same size are said to satisfy an inequality A >= B in the Lowner partial ordering if A-B is nonnegative definite. In this note, we first derive the general solutions in closed-form for the linear matrix equation AXB + (AXB)* = C by using generalized inverses of matrices, and then derive general solutions of the linear matrix inequality AXB + (AXB)* >= C when C is a Hermitian nonnegative definite matrix.

Nyckelord

Linear matrix equation; linear matrix inequality; Lowner partial ordering; general solution; generalized inverses of matrices; rank; inertia

Publicerad i

Mathematical Inequalities and Applications
2012, volym: 15, nummer: 3, sidor: 537-548
Utgivare: ELEMENT

SLU författare

UKÄ forskningsämne

Algebra och logik

Publikationens identifierare

  • DOI: https://doi.org/10.7153/mia-15-47

Permanent länk till denna sida (URI)

https://res.slu.se/id/publ/45204