Let $X=(x_1,\ldots,x_n)\in\mathbb R^{p\times n}$ have independent real columns with finite second moments, not necessarily centered or identically distributed. For $z\in\mathbb C\setminus[0,\infty)$, we compare \[ G^z=\left(\frac1nXX^\top-zI_p\right)^{-1} \] with a deterministic matrix $\tilde G^z$ defined by the second-moment profile $(Σ_i)_{i\in[n]}$, where $Σ_i=\mathbb E[x_ix_i^\top]$. For deterministic matrices \(A\), we prove finite-dimensional \(L^q\) bounds for $\tr(A(G^z-\tilde G^z))$ in terms of moments of centered quadratic forms, without assuming independence among the coordinates of a column. Operator-test bounds impose no trace-growth or aspect-ratio restriction and display explicitly the effect of the sizes and repetitions of the second-moment matrices $(Σ_i)_{i\in[n]}$. Under $\sqrt p\sup_{i\in[n]}|Σ_i|_{\hs}=O(n)$, the Hilbert-Schmidt bounds involve approximation of the profile by commuting positive-semidefinite matrices, with explicit dependence on the approximation error and the dimension of their span. We also obtain corresponding bounds for \(\tr(A G^z B G^z)\), with deterministic \(A,B\). All bounds are locally uniform in $z\in\mathbb C\setminus[0,\infty)$.

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