Geodesic
Operator norms of words formed from positive-definite matrices
The electronic journal of linear algebra, Tome 18 (2009), pp. 13-20.

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

Summary: Let $\alpha 1 , \alpha 2 , . . . , \alpha n , \beta 1 , \beta 2 , . . . , \beta n$ be strictly positive reals with $\alpha 1 + \alpha 2 + \cdot \cdot \cdot + \alpha n = \beta 1 + \beta 2 + \cdot \cdot \cdot + \beta n = s$. In this paper, the inequality |||A $\alpha 1$ B$\beta 1$ A$\alpha 2 \cdot \cdot \cdot A \alpha n$ B$\beta n ||| \leq |$||AB||| s when A and B are positive-definite matrices is studied. Related questions are also studied.
Classification : 15A45
Keywords: positive-definite matrix, matrix power, operator norm, matrix words 
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     author = {Drury, Stephen W.},
     title = {Operator norms of words formed from positive-definite matrices},
     journal = {The electronic journal of linear algebra},
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     volume = {18},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2009__18__a56/}
}
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Drury, Stephen W. Operator norms of words formed from positive-definite matrices. The electronic journal of linear algebra, Tome 18 (2009), pp. 13-20. http://geodesic.mathdoc.fr/item/ELA_2009__18__a56/