Matrix Differential Equation
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 simple matrix ordinary differential equation is
where is an n×1 vector of functions of an underlying variable, is the vector of first derivatives of these functions, and is an n×n matrix, of which all elements are constants.
Note that by using the Cayley-Hamilton theorem and Vandermonde-type matrices, a solution may be given in a simple form. Below it is developed the solution in terms of Putzer's algorithm.
This differential equation has the following general solution:
where, ... and are the eigenvalues of ;, ... and are the respective eigenvectors of and, .... and are constants.
Read more about Matrix Differential Equation: Stability and Steady State of The Matrix System, Solution in Matrix Form, Putzer Algorithm For Computing, Deconstructed Example of A Matrix Ordinary Differential Equation, Solving Deconstructed Matrix Ordinary Differential Equations, Solved Example of A Matrix ODE, See Also
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