Fundamental matrix (linear differential equation)
Matrix consisting of linearly independent solutions to a linear differential equation / From Wikipedia, the free encyclopedia
For other senses of the term, see Fundamental matrix (disambiguation).
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.[1]
Then every solution to the system can be written as , for some constant vector (written as a column vector of height n).
A matrix-valued function is a fundamental matrix of if and only if and is a non-singular matrix for all .[2]