Geodesic
Positive eigenvalues and two-letter generalized words
The electronic journal of linear algebra, Tome 9 (2002), pp. 21-26.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A generalized word in two letters A and B is an expression of the form W = Ao""1Br'1Ao""2Br'2 * * * Ao""N Br'N 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 different (even for 2-by-2 matrices), and this is the focus of the present work.
Classification : 15A18, 15A57
Keywords: positive definite matrices, projections, generalized word 
@article{ELA_2002__9__a22,
     author = {Hillar, C. and Johnson, C.R. and Spitkovsky, I.M.},
     title = {Positive eigenvalues and two-letter generalized words},
     journal = {The electronic journal of linear algebra},
     pages = {21--26},
     publisher = {mathdoc},
     volume = {9},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2002__9__a22/}
}
TY  - JOUR
AU  - Hillar, C.
AU  - Johnson, C.R.
AU  - Spitkovsky, I.M.
TI  - Positive eigenvalues and two-letter generalized words
JO  - The electronic journal of linear algebra
PY  - 2002
SP  - 21
EP  - 26
VL  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ELA_2002__9__a22/
LA  - en
ID  - ELA_2002__9__a22
ER  - 
%0 Journal Article
%A Hillar, C.
%A Johnson, C.R.
%A Spitkovsky, I.M.
%T Positive eigenvalues and two-letter generalized words
%J The electronic journal of linear algebra
%D 2002
%P 21-26
%V 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ELA_2002__9__a22/
%G en
%F ELA_2002__9__a22
Hillar, C.; Johnson, C.R.; Spitkovsky, I.M. Positive eigenvalues and two-letter generalized words. The electronic journal of linear algebra, Tome 9 (2002), pp. 21-26. http://geodesic.mathdoc.fr/item/ELA_2002__9__a22/