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A constant $(n\times n)$-matrix $X(\omega)$ which is the value at $t=\omega$ of the [[Fundamental matrix|fundamental matrix]] $X(t)$, normalized at zero, of a linear system of differential equations

$$\dot x=A(t)x,\quad t\in\mathbf R,\quad x\in\mathbf R^n,$$

with an $\omega$-periodic matrix $A(t)$ that is summable on each compact interval in $\mathbf R$.



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====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  J.K. Hale,   "Ordinary differential equations" , Wiley  (1969)</TD></TR></table>