Fundamental matrix (linear differential equation)
In mathematics, a fundamental matrix of a system of n homogeneous linear ordinary differential equations
is a matrix-valued function whose columns are linearly independent solutions of the system.
Then every solution to the system can be written as, for some constant vector .
One can show that a matrix-valued function is a fundamental matrix of if and only if and is a non-singular matrix for all.The fundamental matrix is used to express the state-transition matrix, an essential component in the solution of a system of linear ordinary differential equations.
