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High Quality Content by WIKIPEDIA articles! In linear algebra, a positive-definite matrix is a (Hermitian) matrix which in many ways is analogous to a positive real number. The notion is closely related to a positive-definite symmetric bilinear form (or a sesquilinear form in the complex case). The distinguishing feature between the real and complex case is that, a bounded positive operator on a complex Hilbert space is necessarily Hermitian, or self adjoint. The general claim can be argued using the polarization identity. That is no longer true in the real case. There is no agreement in the literature on the proper definition of positive-definite for non-Hermitian matrices.