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A matrix difference equation is a difference equation in which the value of a vector (or sometimes, a matrix) of variables at one point in time is related to its own value at one or more previous points in time, using matrices. The order of the equation is the maximum time gap between any two indicated values of the variable vector. For example, or as The most commonly encountered matrix difference equations are first-order.

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rdfs:label	Matrix difference equation (en) 行列差分方程式 (ja)
rdfs:comment	力学系の理論における行列差分方程式（ぎょうれつさぶんほうていしき、英: matrix difference equation）は、各時点においてベクトルとして与えられている変数に関する系で、各時点の値がそれ以前の時点における変数の値と行列を用いた関係性で結ばれているような差分方程式を言う。そのような方程式の階数 (order) とは、変数ベクトルの値を指定するために必要となる任意の二時点の間隔の最大値を言う。例えば、x を n 成分列ベクトル、A, B を n-次正方行列として、は二階方程式の例ということになる。特にこれは右辺に定ベクトル項を持たないから斉次方程式の例でもある。添字をずらしたり、別の文字を用いたりしてやのように書いても方程式としては同じものである。最もよく遭遇する行列差分方程式は、一階のものであろう。 (ja) A matrix difference equation is a difference equation in which the value of a vector (or sometimes, a matrix) of variables at one point in time is related to its own value at one or more previous points in time, using matrices. The order of the equation is the maximum time gap between any two indicated values of the variable vector. For example, or as The most commonly encountered matrix difference equations are first-order. (en)
dcterms:subject	Matrices Linear algebra Recurrence relations Dynamical systems
Wikipage page ID	27567102 (xsd:integer)
Wikipage revision ID	1122572488 (xsd:integer)
Link from a Wikipage to another Wikipage	Quadratic function Algebraic Riccati equation Dynamical system Initial condition Mathematical induction Matrix (mathematics) Matrix inversion Eigenvalue Eigenvalues and eigenvectors Eigenvector Linear difference equation Identity matrix Stability theory Matrix differential equation Matrices Absolute value Linear algebra Recurrence relations Euclidean vector Diagonal matrix Dynamical systems Characteristic equation (calculus) Block matrix Difference equation Exogeny Linear-quadratic-Gaussian control Multi-objective optimization Riccati equation Rational difference equation Zero matrix Matrix Riccati equation
sameAs	Matrix difference equation Matrix difference equation Matrix difference equation Matrix difference equation Matrix difference equation
dbp:wikiPageUsesTemplate	dbt:= dbt:Further dbt:Math dbt:Reflist dbt:Section_link dbt:Su
has abstract	A matrix difference equation is a difference equation in which the value of a vector (or sometimes, a matrix) of variables at one point in time is related to its own value at one or more previous points in time, using matrices. The order of the equation is the maximum time gap between any two indicated values of the variable vector. For example, is an example of a second-order matrix difference equation, in which x is an n × 1 vector of variables and A and B are n × n matrices. This equation is homogeneous because there is no vector constant term added to the end of the equation. The same equation might also be written as or as The most commonly encountered matrix difference equations are first-order. (en) 力学系の理論における行列差分方程式（ぎょうれつさぶんほうていしき、英: matrix difference equation）は、各時点においてベクトルとして与えられている変数に関する系で、各時点の値がそれ以前の時点における変数の値と行列を用いた関係性で結ばれているような差分方程式を言う。そのような方程式の階数 (order) とは、変数ベクトルの値を指定するために必要となる任意の二時点の間隔の最大値を言う。例えば、x を n 成分列ベクトル、A, B を n-次正方行列として、は二階方程式の例ということになる。特にこれは右辺に定ベクトル項を持たないから斉次方程式の例でもある。添字をずらしたり、別の文字を用いたりしてやのように書いても方程式としては同じものである。最もよく遭遇する行列差分方程式は、一階のものであろう。 (ja)
prov:wasDerivedFrom	wikipedia-en:Matrix_difference_equation?oldid=1122572488&ns=0
page length (characters) of wiki page	13337 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Matrix_difference_equation
is Link from a Wikipage to another Wikipage of	Beatrice Meini List of dynamical systems and differential equations topics Dynamical system Initial condition Linear recurrence with constant coefficients Stochastic matrix Leslie matrix System of equations Matrix differential equation Difference Equations: From Rabbits to Chaos List of equations Recurrence relation Attractor Coefficient matrix Riccati equation Rational difference equation Vector autoregression Matrix dynamics
is Wikipage redirect of	Matrix dynamics
is foaf:primaryTopic of	wikipedia-en:Matrix_difference_equation

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