Positive eigenvalues and two-letter generalized words

C. Hillar, C. R. Johnson, I. M. Spitkovsky

Research output: Contribution to journalArticlepeer-review


A generalized word in two letters A and B is an expression of the form W = Aα1Bβ1Aα2Bβ2 ... AαN BβN in which the exponents are nonzero real numbers. When independent positive definite matrices are substituted for A and B, it is of interest whether W necessarily has positive eigenvalues. This is known to be the case when N = 1 and has been studied in case all exponents are positive by two of the authors. When the exponent signs are mixed, however, the situation is quite di.erent (even for 2-by-2 matrices), and this is the focus of the present work.

Original languageEnglish (US)
Pages (from-to)21-26
Number of pages6
JournalElectronic Journal of Linear Algebra
StatePublished - Feb 2002


  • Generalized word
  • Positive definite matrices
  • Projections

ASJC Scopus subject areas

  • Algebra and Number Theory


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