Matrix Inequalities and Twisted Inner Products

  • Thomas H. Pate
Part of the Operator Theory: Advances and Applications book series (OT, volume 202)


We will demonstrate that several known inequalities involving generalized Schur functions, also known as generalized matrix functions, follow from either the Cauchy-Schwartz inequality, or from certain monotonicity relations that exist between inner products on spaces of multilinear functions. Connections between our inner products and permanent inequalities are presented, and a connection to some unresolved problems in partial differential equations is indicated.


Matrix inequalities inner products tensors multilinear functions tensor inequalities 

Mathematics Subject Classification (2000)

15A15 15A45 15A63 15A69 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  • Thomas H. Pate
    • 1
  1. 1.Mathematics DepartmentAuburn UniversityAuburnUSA

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