# Positive eigenvalues and two-letter generalized words

C. Hillar, C. R. Johnson, Ilya Spitkovsky

Research output: Contribution to journalArticle

### Abstract

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 language English (US) 21-26 6 Electronic Journal of Linear Algebra 9 Published - Feb 1 2002

### Fingerprint

Exponent
Eigenvalue
Positive definite matrix
Form

### Keywords

• Generalized word
• Positive definite matrices
• Projections

### ASJC Scopus subject areas

• Algebra and Number Theory

### Cite this

Positive eigenvalues and two-letter generalized words. / Hillar, C.; Johnson, C. R.; Spitkovsky, Ilya.

In: Electronic Journal of Linear Algebra, Vol. 9, 01.02.2002, p. 21-26.

Research output: Contribution to journalArticle

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