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- Green's_matrix abstract "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.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 .This fundamental matrix will provide the homogeneous solution, and if added to a particular solution will give the general solution to the inhomogeneous equation.Let be the general solution. Now,This implies or where is an arbitrary constant vector.Now the general solution is The first term is the homogeneous solution and the second term is the particular solution.Now define the Green's matrix The particular solution can now be written".
- Green's_matrix wikiPageExternalLink ODELS4.
- Green's_matrix wikiPageID "4586351".
- Green's_matrix wikiPageRevisionID "598344517".
- Green's_matrix hasPhotoCollection Green's_matrix.
- Green's_matrix subject Category:Matrices.
- Green's_matrix subject Category:Ordinary_differential_equations.
- Green's_matrix type Abstraction100002137.
- Green's_matrix type Arrangement107938773.
- Green's_matrix type Array107939382.
- Green's_matrix type Communication100033020.
- Green's_matrix type DifferentialEquation106670521.
- Green's_matrix type Equation106669864.
- Green's_matrix type Group100031264.
- Green's_matrix type MathematicalStatement106732169.
- Green's_matrix type Matrices.
- Green's_matrix type Matrix108267640.
- Green's_matrix type Message106598915.
- Green's_matrix type OrdinaryDifferentialEquations.
- Green's_matrix type Statement106722453.
- Green's_matrix comment "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.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 .This fundamental matrix will provide the homogeneous solution, and if added to a particular solution will give the general solution to the inhomogeneous equation.Let be the general solution. ".
- Green's_matrix label "Green's matrix".
- Green's_matrix label "Matrice de Green".
- Green's_matrix sameAs Matrice_de_Green.
- Green's_matrix sameAs m.0cb814.
- Green's_matrix sameAs Q3299258.
- Green's_matrix sameAs Q3299258.
- Green's_matrix sameAs Green's_matrix.
- Green's_matrix wasDerivedFrom Green's_matrix?oldid=598344517.
- Green's_matrix isPrimaryTopicOf Green's_matrix.