 Fundamental matrix of a linear differential equation

For a system of linear differential equations $u^{\prime }=A(t)u$, a fundamental matrix has columns forming a basis of its solution space. It solves $X^{\prime }=A(t)X$ and is invertible at every time in its interval. Every solution is $u(t)=X(t)c$ for a constant vector $c$: differentiating $X^{-1}u$ gives zero. Invertibility at one time implies invertibility throughout the interval by uniqueness of the initial value problem. This notion is distinct from a Markov-chain fundamental matrix or the projective-geometric matrix used in stereo vision.