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A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and of its derivatives of various orders. A matrix differential equation contains more than one function stacked into vector form with a matrix relating the functions to their derivatives. For example, a first-order matrix ordinary differential equation is where is an vector of functions of an underlying variable , is the vector of first derivatives of these functions, and is an matrix of coefficients. where is an constant vector.

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rdf:type	Thing yago:WikicatOrdinaryDifferentialEquations yago:Abstraction100002137 yago:Communication100033020 yago:DifferentialEquation106670521 yago:Equation106669864 yago:MathematicalStatement106732169 yago:Message106598915 yago:Statement106722453
rdfs:label	Sistema de ecuaciones diferenciales (es) Matrix differential equation (en)
rdfs:comment	Un sistema de ecuaciones diferenciales es un conjunto de varias ecuaciones diferenciales con varias funciones incógnitas y un conjunto de condiciones de contorno. Una solución del mismo es un conjunto de funciones diferenciables que satisfacen todas y cada una de las ecuaciones del sistema. Según el tipo de ecuaciones diferenciales puede tenerse un sistema de ecuaciones diferenciales ordinarias o un sistema de ecuaciones en derivadas parciales. (es) A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and of its derivatives of various orders. A matrix differential equation contains more than one function stacked into vector form with a matrix relating the functions to their derivatives. For example, a first-order matrix ordinary differential equation is where is an vector of functions of an underlying variable , is the vector of first derivatives of these functions, and is an matrix of coefficients. where is an constant vector. (en)
rdfs:seeAlso	Matrix exponential
dcterms:subject	Ordinary differential equations
Wikipage page ID	20071404 (xsd:integer)
Wikipage revision ID	1083398218 (xsd:integer)
Link from a Wikipage to another Wikipage	Quadratic equation Derivative Determinant Characteristic polynomial Initial condition Complex numbers Matrix (mathematics) Matrix diagonalisation Matrix difference equation Matrix exponential Matrix multiplication Newton's law of cooling Eigenvalue Eigenvector Eigenvectors Leibniz's notation Linear differential equation MATLAB Identity matrix Stability theory Matrix addition Cayley–Hamilton theorem Trace (mathematics) Wave equation Coefficients Euclidean vector Factorization Fibonacci number Differential equation Gottfried Leibniz Ordinary differential equations Joseph Louis Lagrange Diagonalizable matrix Difference equation Autonomous system (mathematics) Initial value problem Ordinary differential equation Ordinary differential equations Vandermonde matrix Linear equations Linearly independent Vector notation Jordan canonical form Eigenvalues Determinant (mathematics)
sameAs	Matrix differential equation Matrix differential equation Matrix differential equation Matrix differential equation Matrix differential equation
dbp:wikiPageUsesTemplate	dbt:Citation_needed dbt:Math dbt:Mvar dbt:Reflist dbt:See_also dbt:Short_description
has abstract	Un sistema de ecuaciones diferenciales es un conjunto de varias ecuaciones diferenciales con varias funciones incógnitas y un conjunto de condiciones de contorno. Una solución del mismo es un conjunto de funciones diferenciables que satisfacen todas y cada una de las ecuaciones del sistema. Según el tipo de ecuaciones diferenciales puede tenerse un sistema de ecuaciones diferenciales ordinarias o un sistema de ecuaciones en derivadas parciales. (es) A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and of its derivatives of various orders. A matrix differential equation contains more than one function stacked into vector form with a matrix relating the functions to their derivatives. For example, a first-order matrix ordinary differential equation is where is an vector of functions of an underlying variable , is the vector of first derivatives of these functions, and is an matrix of coefficients. In the case where is constant and has n linearly independent eigenvectors, this differential equation has the following general solution, where λ1, λ2, …, λn are the eigenvalues of A; u1, u2, …, un are the respective eigenvectors of A; and c1, c2, …, cn are constants. More generally, if commutes with its integral then the general solution to the differential equation is where is an constant vector. By use of the Cayley–Hamilton theorem and Vandermonde-type matrices, this formal matrix exponential solution may be reduced to a simple form. Below, this solution is displayed in terms of Putzer's algorithm. (en)
prov:wasDerivedFrom	wikipedia-en:Matrix_differential_equation?oldid=1083398218&ns=0
page length (characters) of wiki page	15054 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Matrix_differential_equation
is Link from a Wikipage to another Wikipage of	List of named differential equations Matrix difference equation Matrix exponential Eigenvalue perturbation Controllability Linear dynamical system Partial differential equation List of equations Jacobian matrix and determinant Coefficient matrix Discrete Laplace operator Ordinary differential equation Observability Matrix Differential Equation
is Wikipage redirect of	Matrix Differential Equation
is foaf:primaryTopic of	wikipedia-en:Matrix_differential_equation

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