zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the exponential metric increasing property. (English) Zbl 1052.15013
A short and beautifully simple matrix theoretical proof of the negative curvature of the set of positive definite real or complex matrices P is given. It is based on the exponential operator of a matrix, the exponential metric increasing property, and the logarithmic mean and geometric-arithmetic mean inequalities for scalars and matrices. The Riemannn metric is studied on the manifold P of positive definite matrices, as well as a generalized exponential metric increasing property for symmetric gauge functions Φ. Consequently P is shown to also be a metric space of non-positive curvature in any Finsler metric δ Φ . The last section derives the Golden-Thompson inequality from these results and investigates related majorization results.

MSC:
15A45Miscellaneous inequalities involving matrices
15A48Positive matrices and their generalizations (MSC2000)
15A60Applications of functional analysis to matrix theory
53B21Methods of Riemannian geometry
53B40Finsler spaces and generalizations (areal metrics)