2 insert citation edited Feb 9 '17 at 17:13 Christian Clason 11k33 gold badges3737 silver badges6262 bronze badges According to the paper "Computing a nearest symmetric positive semidefinite matrix" Nicholas J. Higham, MR 943997 Computing a nearest symmetric positive semidefinite matrix, Linear Algebra Appl. 103 (1988), 103--118, one of the solution is in the following form, $$A_{opt} = S + |\lambda| I$$ where $$I$$ is the identity matrix, $$\lambda$$ is the smallest negative eigenvalue of $$S$$ According to the paper "Computing a nearest symmetric positive semidefinite matrix" (1988), one of the solution is in the following form, $$A_{opt} = S + |\lambda| I$$ where $$I$$ is the identity matrix, $$\lambda$$ is the smallest negative eigenvalue of $$S$$ According to the paper Nicholas J. Higham, MR 943997 Computing a nearest symmetric positive semidefinite matrix, Linear Algebra Appl. 103 (1988), 103--118, one of the solution is in the following form, $$A_{opt} = S + |\lambda| I$$ where $$I$$ is the identity matrix, $$\lambda$$ is the smallest negative eigenvalue of $$S$$ 1 answered Feb 9 '17 at 15:12 Kai 2122 bronze badges According to the paper "Computing a nearest symmetric positive semidefinite matrix" (1988), one of the solution is in the following form, $$A_{opt} = S + |\lambda| I$$ where $$I$$ is the identity matrix, $$\lambda$$ is the smallest negative eigenvalue of $$S$$