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About: Green's matrix     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatMatricesyago:WikicatOrdinaryDifferentialEquationsyago:Abstraction100002137yago:Arrangement107938773yago:Array107939382yago:Communication100033020yago:DifferentialEquation106670521yago:Equation106669864yago:Group100031264yago:MathematicalStatement106732169yago:Matrix108267640yago:Message106598915yago:Statement106722453yago:WikicatDifferentialEquations New Facet based on Instances of this Class

In mathematics, and in particular ordinary differential equations, a Green's matrix helps to determine a particular solution to a first-order inhomogeneous linear system of ODEs. The concept is named after George Green. For instance, consider where is a vector and is an matrix function of , which is continuous for , where is some interval. Now let be linearly independent solutions to the homogeneous equation and arrange them in columns to form a fundamental matrix: Now is an matrix solution of . Let be the general solution. Now, This implies or where is an arbitrary constant vector.