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 an interconnection between the Lipschitz continuity of the solution map and the positive principal minor property in linear complementarity problems over Euclidean Jordan algebras. (English) Zbl 1138.90033
Let V be an Euclidean Jordan algebra, K be a symmetric cone in V, L:VV be a linear transformation and qV. The linear complementary problem associated to L and q, LCP(L,q), prescribes finding xV such that xK, Lx+qK and x,Lx+q=0. It is well known that when V= n and L is a real matrix, LCP(L,q) has a unique solution for all q n , iff all the principal minors of L are positive. In this case the solution map of the LCP(L,q) is well defined and Lipschitz continuous in n . The main result of this paper establishes one direction of the analogous property in the general case: if the solution map is Lipschitz continuous and if L has the Q-property, then L has the positive principal minor property.
MSC:
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
17C30Automorphisms and other operators on Jordan algebras
17C50Jordan structures associated with other structures