Positive Semidefiniteness (PSD) Definition(Positive Semidefiniteness): A symmetric square matrix A E R"x is said to be positive semidefinite,denoted A>≥0，ifVx∈R”,xTAx≥0. Theorem: For symmetric A E R"X",the followings are equivalent: ·A≥0 all eigenvalues(A)≥0 ·A=BB for some B∈RnxnPositive Semidefiniteness (PSD) Definition (Positive Semidefiniteness): A symmetric square matrix is said to be positive semidefinite, denoted , if , . A ∈ ℝn×n A ≽ 0 ∀x ∈ ℝn xTAx ≥ 0 Theorem: For symmetric , the followings are equivalent: • • all eigenvalues • for some A ∈ ℝn×n A ≽ 0 λ(A) ≥ 0 A = BTB B ∈ ℝn×n