zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Extreme ranks of real matrices in solution of the quaternion matrix equation AXB=C with applications. (English) Zbl 1188.15016
Summary: For a consistent quaternion matrix equation AXB=C, the formulas are established for maximal and minimal ranks of real matrices X 1 ,X 2 ,X 3 ,X 4 in solution X=X 1 +X 2 i+X 3 j+X 4 k. A necessary and sufficient condition is given for the existence of a real solution of the quaternion matrix equation. The expression is also presented for the general solution to this equation when the solvability conditions are satisfied. Moreover, necessary and sufficient conditions are given for this matrix equation to have a complex solution or a pure imaginary solution. As applications, the maximal and minimal ranks of real matrices E,F,G,H in a generalized inverse (A+Bi+Cj+Dk) - =E+Fi+Gj+Hk of a quaternion matrix A+Bi+Cj+Dk are also considered. In addition, a necessary and sufficient condition is derived for the quaternion matrix equations A 1 XB 1 =C 1 and A 2 XB 2 =C 2 to have a common real solution.
15A24Matrix equations and identities
15A33Matrices over special rings
15A03Vector spaces, linear dependence, rank
15A09Matrix inversion, generalized inverses