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In this paper, we view matrix frames as representations of quivers and studythem within the general framework of quiver invariant theory. We are thus ledto consider the large class of semi-stable matrix frames. Within this class, weare particularly interested in radial isotropic and Parseval matrix frames.  Using methods from quiver invariant theory [CD19], we first prove a farreaching generalization of Barthe's Radial Isotropy Theorem [Bar98] to matrixframes (see Theorems 1(3) and 29). With this tool at our disposal, we provide aquiver invariant theoretic approach to the Paulsen problem for matrix frames.We show in Theorem 2 that for any given $\varepsilon$-nearly equal-normParseval frame $\mathcal{F}$ of $n$ matrices with $d$ rows there exists anequal-norm Parseval frame $\mathcal{W}$ of $n$ matrices with $d$ rows such that$\mathsf{dist}^2(\mathcal{F},\mathcal{W})\leq 46 \epsilon d^2$.

A quiver invariant theoretic approach to Radial Isotropy and Paulsen's Problem for matrix frames