正定矩阵

An advantage of this method is that it can be applied when the covariance matrix of the invested projects is positive semi-definite.

该方法的优点在于能够处理各投资项目之间的协方差矩阵为半正定的情形。

The acoustical radiation power is expressed as a Hermitian quadratic form, while the radiation modes is determined by general eigenvalue decomposing, and then the radiation efficiency is computed via the orthodoxy of radiation modes with regards to impedance matrix and average velocity matrix; lastly, the validity of the method is proved by pulsating sphere and radiating cube with analytical results.

先将结构的声辐射功率表示为一个正定的厄米特二次型，运用广义特徵值分解求解了复杂结构的声辐射模态，然后利用声辐射模态关于阻抗矩阵与均方速度祸合矩阵的正交性，求解了复杂结构的声辐射效率，最后用具有解析解的脉动球与辐射立方体验证了该方法的有效性。

According to the studied results at present, the studied objects are mainly thin plate and beam about sound radiation mode, a method computed sound radiation mode of complex structure is presented in this dissertation, according to the results of the previous two chapter, a theoretical method to solve acoustical radiation mode and acoustical radiation efficiency of complex structure by boundary element method and acoustical radiation theory is posed, the acoustical radiation power is expressed as a Hermitian quadratic form, while the radiation modes is determined by general eigenvalue decomposing, and then the radiation efficiency is computed via the orthodoxy of radiation modes with regard to impedance matrix and average velocity matrix; lastly, the validity of the method is proved by pulsating sphere and radiating cube with analytical results. According to results of the form three chapter, the structure sound radiation sensitivity is studied in detail, the sound radiation power of structure can be expressed as positive Hermitian quadratic form, the sound radiation sensitivity can be expressed as two parts by partial differential with respect to design variable, which are sensitivity of boundary velocity and impedance matrix, combined with the theory of FEM and BEM, the structure sound radiation can be translated to the analysis of structure dynamic sensitivity and impedance matrix sensitivity. The theory posted in this dissertation is tested by the FEM software ANSYS and the software AAS programmed by author.

在前几章的基础上，通过结构声辐射的模态理论对结构的声辐射的机理进行了深入地探讨，针对目前声辐射模态的研究对象主要是简单的板和梁类结构，提出了一种计算复杂结构声辐射模态的方法，利用前两章研究所得的结论，将边界元方法与广义特征值的理论结合起来研究了复杂结构的声辐射模态与声辐射效率，先将结构的声辐射功率表示为一个正定的厄米特二(来源：ABb7C论文0909网www.abclunwen.com)次型，运用广义特征值分解求解了复杂结构的声辐射模态，然后利用声辐射模态关于阻抗矩阵与均方速度耦合矩阵的正交性，求解了复杂结构的声辐射效率，最后用具有解析解的脉动球与辐射立方体验证了该方法的有效性。

From the matrix theory and the general principle of the iterative convergence of the linear coupled equations, this dissertation firstly proved the sufficient necessary convergent conditions for CMAC batch learning as well as the necessary convergent conditions for CMAC incremental learning, in which no additive conditions were needed. The past researchers'conclusions under the special condition of the positive articulation matrix are generalized and improved.

从矩阵理论和线性方程组迭代收敛的一般性原理出发，首次在不附加特殊条件的情况下，证明了CMAC学习算法在批量和增量两种学习方式下收敛的一般性定理，给出CMAC算法在批量学习方式下收敛的充要条件，以及在增量学习方式下收敛的必要条件，对前人在关联矩阵正定的特殊条件下得出的结论进行了推广和改进。

Positive semi-definite matrices are positive definite if and only if they are nonsingular.

正半定矩阵是正定的，当且仅当它们是非奇异矩阵。

By applying these two tools,we mainly discuss the problems as follows:1 Perturbation identities for the generalized polar decomposition:By applying singular value decomposition, we study the perturbation bounds of the generalized polar decomposition under unitary invariant norms when A is perturbed by addition or multiplication,respectively and give our bounds in identities.2 A class of new unitary invariant metrics: This paper generalized a class of new unitarily invariant metrics and give the upper-bounds and lower-bounds by C-S decomposition.

利用这两个强有力的工具，本文主要讨论了如下问题：1 矩阵广义极分解的扰动等式：利用奇异值分解，本文分别讨论了加法扰动和乘法扰动下矩阵广义极分解在任意酉不变范数下的扰动界，并首次以恒等式的形式给出了酉极因子和半正定因子的扰动界。2 一类新的酉不变度量：本文推广了文[22] 中的结论，定义了一类新的酉不变度量。

The physical meaning of the dynamical equilibrium relationships, velocity space-time distribution and energy propagation involved in the energy matrices can be described by the positive definite quadratic form of the energy matrices.

能量矩阵蕴含的动态力的平衡关系、速度的时间_空间分布和能量的传播及变化的物理意义，能够从能量矩阵的正定二次型特性表述出来。

Buckley, and discusses the fuzzy eigenvalue problem of real symmetric positive fuzzy matrix.

Buckley定义的模糊矩阵为研究对象，全面地讨论了实对称正定模糊矩阵的有关模糊特征值的问题。

Under the helix boundary condition, the Helmhotz matrix has Toeplitz structure with positive definite property.

在螺旋边界条件下，该矩阵H具有Toeplitz结构的正定厄密矩阵，其快速求逆可由谱法LU分解或直解法快速实现。

A numerical algorithm and a numerical experiment are given. 2. The least norm, positive semidefinite and positive definite real solutions of bisymmetric matrix equations (A~TXA, XA — YAD)=(D, 0)are considered by applying the generalized singular value decomposition.

利用广义奇异值分解讨论了矩阵方程(A~T XA，XA-YAE)=(E，0)在对称次反对称矩阵集合中的解、极小范数解和在双对称矩阵集合中的解、极小范数解及正定解； 3。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷