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)
Transition matrix and generalized matrix exponential via the Peano-Baker series. (English) Zbl 1093.39017
Using generalized form of the Peano-Baker series, the author gives a closed form of the transition matrix for the linear system $x^\Delta (t) = A(t) x(t)$ on an arbitrary time scale $\mathbb{T}$ (i.e., some nonempty closed subset of the real axis $\mathbb{R}$), where $A(t)$ is an $n \times n$ matrix function, $x^\Delta (t)$ is so-called delta derivative. When $A(t) \equiv A$ is a constant matrix then the transition matrix has the form of a generalized matrix an exponential on the time scale. Using the generalized Laplace transform, an explicit representation of the time scale matrix exponential is obtained. It is shown that the matrix exponential can be expressed also as a finite sum of powers of the matrix $A$ with infinitely delta differentiable functions as coefficients.

39A12Discrete version of topics in analysis
34A30Linear ODE and systems, general
Full Text: DOI