Positive Definite, Semidefinite
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Mathematics/Linear Algebra
Positive Definite, Semidefinite Definition 1. Let T∈L(V)T∈L(V) where VV is a finite-dimensional inner product space, and let A∈Mn×n(F)A∈Mn×n(F). Then TT is called positive definite [positive semidefinite] if TT is hermitian and ⟨T(x),x⟩>0⟨T(x),x⟩>0 [⟨T(x),x⟩≥0],∀x≠0[⟨T(x),x⟩≥0],∀x≠0, and AA is called positive definite [positive semidefinit..