positive definite matrix
对于任意非零向量x
常用释义
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基本释义
- 正定矩阵：在线性代数中，指具有特定性质的一种矩阵。如果一个矩阵M是对称的，并且所有的特征值都是正数，那么它被称为正定矩阵。换句话说，对于任意非零向量x，二次型x^T M x始终是正数。正定矩阵在数学和工程的各个领域中有重要的应用，如优化、数值分析和控制理论。
例句
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1·Results linear complementary problem have unique solution when m is generalized positive definite matrix.结果得到了当m是广义正定矩阵时，线性互补问题存在唯一解。
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2·It wishes to find a new way for normative research into the concept of generalized positive definite matrix.希望为广义正定矩阵概念的规范化探出一条新路。
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3·Positive definite matrix occupies a very important position in matrix theory, and has great value in practice.正定矩阵在矩阵论中占有十分重要的地位，在实际中也有广泛的应用价值。
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4·In this paper, some important inequalities on norm of determinent of complex positive definite matrix and its Schur complement are obtained.正定复矩阵是矩阵论中的一个重要概念，人们已经掌握了它的若干性质与结构。
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5·In this paper, we discuss properties of positive definite complex matrix, and the relation between it and the Hermite positive definite matrix.本文给出了全正定矩阵的概念，讨论了全对称实矩阵是全正定矩阵的几个充分必要条件。
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6·The principal submatrix of the asymmetrical generalized positive definite matrix is not asymmetrical generalized positive definite matrix in general.指出非对称广义正定矩阵的主子矩阵一般不是非对称广义正定矩阵。
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7·General solutions of above inverse problem in positive definite matrix and in orthogonal matrix are given here by using factorization method of matrix.本文用矩阵分解法给出该反问题在正定矩阵类及正交矩阵类中的通解。
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8·And then the eigenvalue problem of integral equation is transformed into the standard eigenvalue problem of a positive definite matrix with infinite order.进而将积分方程形式的特征值问题转化为无穷阶正定对称矩阵的标准特征值问题。
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9·To in this paper, the definition of complex generalized positive definite matrix is given, its fundamental properties are studied, and its equivalent characteristics are established.当引入广义正定复矩阵这个概念之后，也应该讨论它相应的性质与结构，这对丰富矩阵论的内容无疑是有意义的。
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10·Some equivalent representations of complex positive semi definite matrices are given by using equivalent conditions of positive semi definite of real symmetric matrix.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。