对角化

The pupose of the research is to develops public key encryption and digital signature shemes based on matrix canonical decomposition problem, or matrix diagonalization problem over Z/n, the ring of integers with modulo-n addition and multiplication in particular, where n is an RSA modulus.

本课题研究基于矩阵经典分解问题，特别是Z/n上矩阵对角化问题的公钥密码与数字签名算法，其中n是一个RSA模数。新算法采用由一个矩阵多项式构成的多维单向陷门函数，其单向性由矩阵对角分解问题(即通过相似变换将矩阵化为对角型的问题)的复杂性来保障，对该函数求逆的陷门由矩阵的特征值或特征向量提供。

Additionally, we propose an algebraic diagonalization method which is equivalent to Bogoliubov-Valatin transformation in a sense.

此外，我们介绍了一种新的对角化方法——代数对角化，它在一定程度上等价于Bogoliubov变换。

Successive diagonalization and truncation technique was used to reduce the size of the final Hamiltonian matrix to be diagonalized.

为了降低需要对角化的最终哈密顿矩阵的维数，采用连续对角化截断方法。

This paper discusses the matrix of the basic theory of diagonalization. On this basis, it studies the two matrices at the same time or a contract similar to the conditions of diagonalization.

本文论述了矩阵可对角化的基本理论，在此基础上研究了两个矩阵同时相似或合同对角化的条件。

In this paper, the concept of congruent diagonalization of matrix is presented, and the problem of diagonalization of one matrix is generalized.

提出矩阵合同对角化概念，对一个矩阵对角化问题进行推广思考，讨论了二个矩阵的同时对角化问题，取得了一些结果，给出了有关算

Furthermore, we express a real quaternionic polynomial with four general polynomials which have real coefficients, thus build direct relation between real quaternionic polynomials and general polynomials.

新方法以四元数的复表示及其可对角化的特征结构为理论基础，将问题等价为求解2×2矩阵多项式的可对角化解；进一步将四元数多项式用四个实系数多项式表示，建立了四元数多项式与一般多项式的直接关联。

It is also pointed out that an n-mode boson coupled quadratic Hamiltonian can be diagonalized by a "negative unitary" matrix which is an element of complex symplectic group SP(2n,c),and an n-mode fermion coupled quadratic Hamiltonian can be diagonalized by a unitary matrix which is an element of complex fermion group F(2n,c).

并且指出，对于n模玻色子耦合二次型哈密顿量，通过一个负幺正矩阵它是复辛群SP(2n，c的元素可以把它对角化；对n模费米子耦合二次型哈密顿量，通过一个幺正矩阵它是复费米群F(2n，c的元素可以把它对角化。

To one quaternion matrix, according to its normal form, into which a quaternion matrix is transformed after decomposed, the types of decomposition of a quaternion matrix are divided into three large classes: diagonalized decomposition, triangular decomposition and triangular-diagonalized decomposition.

对单个四元数矩阵，以分解后的四元数矩阵的标准型作为分类的标准，将四元数矩阵的分解分为三大类：对角化分解、三角化分解、三角一对角化分解。

Tridiagonalization of symmetric matrices and computing eigenvalues of tridiagonal symmetric matrix are the keys of eigenproblem parallel solver of dense symmetric matrix.

对称矩阵三对角化和三对角对称矩阵的特征值求解是稠密对称矩阵特征问题并行求解器的关键步。

Then, the relation between vibration and sound, the acoustic holography method, the indeterminacy and identifiability of BSS, the BSS algorithm are discussed in detail. Based on above researches, the dissertation is divided in following four sections. The first section investigates the BSS algorithm suitable to acoustic feature separation. The algorithm of the joint approximate diagonalization of eigen-matrices is proposed. The spectra or the time-frequency distributions of source signals are the interesting features in ABD and they are separated from mixing signals by JADE algorithm. Then, the convolutive mixing model is transformed into a high-dimension instantaneous mixing model, and the deconvolution of source signals is achieved by the joint approximate block diagonalization of eigen-matrices. The proposed algorithm has a global minimum, and it is unsensitive to noise interference.

论文首先概述国内外声学诊断研究进展与盲分离研究进展，给出机器噪声声场与盲分离的数学描述，讨论了声振辐射、声全息、盲分离模型、盲分离可解性、盲分离结果不确定性、分离算法等基本问题，在此基础上，论文的研究工作分为以下四个部分：第一部分研究适用于声学特征分离的盲分离算法，提出基于特征提取的联合近似对角化盲分离算法，该算法以频谱特征或时频特征作为分离目标，从混合信号中分离源信号频谱特征或时频特征，最大限度地保留了与声学特征提取有关的频谱特征或时频特征，采用模型变换把卷积混合模型变换为一个高维瞬时混合模型，通过联合近似分块对角化算法实现源信号频谱特征与时频特征的盲反卷积。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。