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A matrix difference equation〔Cull, Paul; Flahive, Mary; and Robson, Robbie. ''Difference Equations: From Rabbits to Chaos'', Springer, 2005, chapter 7; ISBN 0-387-23234-6.〕〔Chiang, Alpha C., ''Fundamental Methods of Mathematical Economics'', third edition, McGraw-Hill, 1984: 608–612.〕 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. Occasionally, the time-varying entity may itself be a matrix instead of a vector. 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. ==Non-homogeneous first-order matrix difference equations and the steady state== An example of a non-homogeneous first-order matrix difference equation is : with additive constant vector ''b''. The steady state of this system is a value ''x *'' of the vector ''x'' which, if reached, would not be deviated from subsequently. ''x *'' is found by setting in the difference equation and solving for ''x *'' to obtain : where is the ''n×n'' identity matrix, and where it is assumed that is invertible. Then the non-homogeneous equation can be rewritten in homogeneous form in terms of deviations from the steady state: : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「matrix difference equation」の詳細全文を読む スポンサード リンク
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