We study the eigenvalue distribution and resolvent of a Kronecker-product random matrix model , where are independent Wigner matrices and are deterministic and diagonal. For fixed spectral arguments, we establish a quantitative approximation for the Stieltjes transform by that of an approximating free operator, and a diagonal deterministic equivalent approximation for the resolvent. We further obtain sharp estimates in operator norm for the resolvent blocks, and show that off-diagonal resolvent entries fall on two differing scales of and depending on their locations in the Kronecker structure. Our study is motivated by consideration of a matrix-valued least-squares optimization problem subject to a linear constraint. For random instances of this problem defined by Wigner inputs , our analyses imply an asymptotic characterization of the minimizer and its associated minimum objective value as .
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