Before revision:  B \|_F^2 = \sum_{i : \lambda_i(A) < 0 \lambda_i^2(A) } > \epsilon n^2  \succeq 0 denotes that \mathbf{B} is PSD} . Our main algorithmic contribution is a non-adaptive tester which distinguishes between these cases using only \tilde{O}(1/\epsilon^4) queries to the entries of A. For the related "\ell_\infty-gap problem", where A is either PSD or has an eigenvalue satisfying \lambda_i(A) <\succeq 0} \|\mathbf{A}} - \epsilon n, our algorithm only requires\|_2 > \epsilon n.
After revision:  B \|_F^2 = \sum_{i : \lambda_i(A) < 0 \lambda_i^2(A) } > \epsilon n^2 \succeq 0 denotes that \mathbf{B} is PSD} . Our main algorithmic contribution is a non-adaptive tester which distinguishes between these cases using only \tilde{O}(1/\epsilon^4) queries to the entries of \mathbf{A "\ell_\infty-gap problem", where A is either PSD or has an eigenvalue satisfying \lambda_i(A) <\succeq 0} \|\mathbf{A}} - \epsilon n, our algorithm only requires\|_2 > \epsilon n.