Inequalities for sums of matrix quadratic forms

Kenneth Nordström, Thomas Mathew

Research output: Contribution to journalArticlepeer-review


An attainable upper matrix bound is derived for Σmk=1 (C + U1 + ... +Uk)-1Uk(C + U1 + ... + Uk)-1, improving upon earlier bounds by Anderson and Taylor [Linear Algebra Appl. 30:93-99 (1980)] and Olkin [Linear Algebra Appl. 52/53:529-532 (1983)]. Inequalities for the sum of harmonic means or parallel sums are derived as special cases. The more general problem of obtaining an upper bound for Σmk=1 (C + U1 + ... + Uk)-pUk(C + U1 + ... + Uk)-p is also considered.

Original languageEnglish
Pages (from-to)429-447
Number of pages19
JournalLinear Algebra and Its Applications
Publication statusPublished - Apr 1996

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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