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The dynamical system under consideration is \begin{align*} &u_{tt}-u_{xx}+Vu=0,\qquad x>0,\,\,\,t>0;\\ &u|_{t=0}=u_t|_{t=0}=0,\,\,x\geqslant 0;\quad u|_{x=0}=f,\,\,t\geqslant 0,\end{align*} where $V=V(x)$ is a matrix-valued function ({\it potential});$f=f(t)$ is an $\mathbb R^N$-valued function of time ({\it boundary control});$u=u^f(x,t)$ is a {\it trajectory} (an $\mathbb R^N$-valued function of $x$ and$t$). The input/output map of the system is a {\it response operator}$R:f\mapsto u^f_x(0,\cdot),\,\,\,t\geqslant0$.  The {\it inverse problem} is to determine $V$ from given $R$. To characterizeits data is to provide the necessary and sufficient conditions on $R$ thatensure its solvability.  The procedure that solves this problem has long been known and thecharacterization has been announced (Avdonin and Belishev, 1996). However, theproof was not provided and, moreover, it turned out that the formulation mustbe corrected. Our paper fills this gap.

Data characterization in dynamical inverse problem for the 1d wave equation with matrix potential