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    A minimization problem

    I have this matrix problem: Given R_1, R_2, R_3\in\mathbb{R}^{N\times N} are symmetric matrices with rank p<N. Their SVD are U_1\Sigma_1 U_1^T, U_2\Sigma_2 U_2^T and U_3\Sigma_3 U_3^T, respectively. I want to find a rank p matrix V such that J = \|V\Sigma_1 V^T - U_1\Sigma_1 U_1^T\|_F^2 +...
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