### Abstract

A generalized word in two letters A and B is an expression of the form W = A^{α1}B^{β1}A^{α2}B^{β2} ... A^{αN} B^{βN} 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) |
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Pages (from-to) | 21-26 |

Number of pages | 6 |

Journal | Electronic Journal of Linear Algebra |

Volume | 9 |

DOIs | |

State | Published - Feb 2002 |

### Keywords

- Generalized word
- Positive definite matrices
- Projections

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Hillar, C., Johnson, C. R., & Spitkovsky, I. M. (2002). Positive eigenvalues and two-letter generalized words.

*Electronic Journal of Linear Algebra*,*9*, 21-26. https://doi.org/10.13001/1081-3810.1069