= Fundamental matrix of a linear differential equation
{title2=$X'=A(t)X,\quad\det X\ne0$}
= Fundamental matrix
{synonym}
For a system of <linear differential equations> $u'=A(t)u$, a fundamental matrix has columns forming a <basis> of its solution space. It solves $X'=A(t)X$ 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.
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