给出了实部半正定矩阵的一种判定方法，并给出了该判定方法的算法。
A criterion for the real part positive semidefiniteness matrix is presented, and the algorithm for this criterion is given.
借助矩阵的合同变换法，给出了化实二次型为标准形的方法、求标准正交基的方法，并给出了正定二次型判定定理的新证明。
By means of congruent transformation in matrix, the method of transforming real quadratic form into standard form and the method of normal orthogonal basis are given in this paper.
利用实对称矩阵的半正定之等价条件给出了复正半定矩阵的几个等价条件。
Some equivalent representations of complex positive semi definite matrices are given by using equivalent conditions of positive semi definite of real symmetric matrix.
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