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)
Symmetric word equations in two positive definite letters. (English) Zbl 1038.15005

Consider the word equation S(A,B)=P where A,B,P are positive definite complex Hermitian n×n-matrices, A is the unknown matrix, and S(A,B) is a symmetric (“palindromic”) generalized word of the form W=A p 1 B q 1 ...A p k B q k A p k+1 ; here p i ,q i * , i=1,...,k, p k+1 . “Symmetric” means that W=A p k+1 B q k A p k ...B q 1 A p 1 .

The authors show that every symmetric word equation is solvable and they conjecture uniqueness of the solution. In some cases the solution is unique (example: the unique solution of the equation ABA=P is A=B -1/2 (B 1/2 PB 1/2 ) 1/2 B -1/2 ); in general, uniqueness is an open question. If B and P are real, then one can find a real solution A as well. The notion of symmetric word is generalized to allow non-integer exponents, with certain limitations. Applications and methods for finding solutions are also discussed.


MSC:
15A24Matrix equations and identities
15A57Other types of matrices (MSC2000)
15A18Eigenvalues, singular values, and eigenvectors
15A90Appl. of matrix theory to physics (MSC2000)