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  (written as a column vector of height ). 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

Control theory
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. See also
Linear differential equation
Liouville's formula
Systems of ordinary differential equations

References

Matrices
Differential calculus