本文系统的研究了四元数矩阵分解理论。
In this paper, decomposition of a quaternion matrix is systemically studied.
本文讨论四元数矩阵右特征值的存在性问题。
In this paper, we study the existence for right eigenvalue of quaternion matrix.
研究四元数矩阵的主谱、协谱和奇异谱的性质。
The main spectrums, singular spectrums and cospectrums of matrices over quaternionic sfield are studied.
给出了自共轭四元数矩阵的弱圈积的特征值的一些不等式。
Some inequalities of eigenvalues for weak cycle products of self-conjugate quaternion matrices are given.
本文给出了四元数矩阵函数的定义，讨论了四元数矩阵函数的一些性质。
This paper discusses the definition and properties for functions of quaternion matrix.
本文获得了四元数矩阵的范数和迹的一些不等式，改进了近期的某些结果。
In this paper, we obtain some inequalities for norm and traces of quaternion matrices.
四元数矩阵方程则是研究四元数量子力学理论中相应的数学物理模型的基础。
The quaternion matrix equation is studies in the quaternion quantum-mechanical theory of the corresponding mathematics physical model foundation.
同时得到一些关于四元数矩阵的性质，以及体上矩阵相似和合相似的充要条件。
Finally, the necessary and sufficient condition is shown for similarity and consimilarity of matrices over quaternion field.
利用与每个四元数矩阵相关联的复伴随矩阵，问题被简化为关于复数矩阵的并行问题。
The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each quaternion matrix.
近30年来，许多专家学者对四元数矩阵进行了广泛的研究，取得了丰硕的理论成果。
In recent 30 years, many experts and scholars were carrying on an extensive research about quaternionic matrix and got plenteous theoretical results.
证明了几个与四元数矩阵迹有关的弱控制不等式，推广、改进了有关文献的相应结果。
Several weakly controled inequalities with relation to trace of quaternions matrices are proved, and relevant results in some references are generalized and improved.
定义了四元数矩阵的范数，并利用范数的性质，建立了几个四元数矩阵之迹的不等式。
The definition of norm of quaternion matrices is given, and several inequalities on the traces of quaternion matrices are proved by using properties on the norm of quaternion matrices.
我们提出了“指标分布图”的新概念，从而构造出一个估计任意维数矩阵乘法的新算法。
We propose a new conception: Index Distribution Chart, which makes it possible for us to construct a new fast multiplication algorithm for matrix pairs of arbitrary dimensions.
本文研究了四元数量子力学中一类要求其解是正规或可对角化四元数矩阵的特征值反问题。
One kind of inverse eigenvalue problems, whose solutions are required to be normal or diagonalizable matrices, is investigated in quaternionic quantum mechanics.
为此给出了解四元数矩阵微分方程的一个强有力的算式，并给出了详细的数学推导和证明。
The mathematical deduction and confirmation of the algorithm are introduced in the paper, which is a powerfully effective one for solving the quaternion matrix differential equation.
本文提出一种改进边界元法，它使形成的边界元方程不隐含本征量，避免大阶数矩阵的转置。
A modified boundary element method is proposed. In the approach, the matrices in the formed boundary equation implicitly contain no eigen parameter.
通过对四元数和四元数矩阵理论的历史与现状的考查，我们发现，从1843年英国数学家W 。
Through the research on the history and actuality of the quaternion and the quaternion matrix theory , we have found that , from 1843, when English mathematician W.
由于四元数矩阵的酉相合与酉相似有着密切联系，本文还讨论了四元数矩阵的酉相似的一些性质。
Since unitary congruence of quaternion matrices is in connection with unitary similarity of quaternion matrices, we also discuss some properties of the unitary similarity of quaternion matrices.
摘要研究了四元数矩阵分解为两个自共轭矩阵乘积，其中有一个是非奇异阵的条件，得到了一些有用的结果。
It is studied factorizing a matrix over quaternion field to the product of two self - conjugate matrices . and some useful results are obtained.
增广向量法通过扩充输入、状态、输出等向量的维数及系统系数矩阵维数构造增广系统，使复杂问题简单化。
An augmenting system is designed to extend dimension of input, state, output and the coefficient matrixes in the method of augmenting vectors in order to predigest complicated problem.
证明了对每一个四元数矩阵，至少存在一个右特征主值，存在一个属于它的特征向量，并给出了具体的求解方法。
We proved that each square quaternion matrix has at least one right characteristic principal value and its eigenvector, and a concrete solution was given.
给出了四元数矩阵加权广义逆的表达式，回答了关于四元数矩阵加权（3，4）和（2，4）逆表达式的公开问题。
The expression of the weighted generalized inverse of quaternion matrices are expressed, and the open question on the characterization of the (3,4) and (2,4) inverse are solved.
利用四元数矩阵的加权共轭转置定义了四元数矩阵的加权左（右）序，给出了加权左（右） 序的一些等价刻画，推广了以往文献的相应结果。
The weighted right (left) star partial ordering is defined though the weighted conjugate of the matrix , some characterisation of its is obtained, the existed results are extended.
杂志的创刊号上发表的论文包含话题广泛，从图像增强到矩阵的状态数(关于这个话题不要问我太多)都有所涉及。
The inaugural issue includes topics ranging from image enhancement to condition Numbers of matrices (don't ask).
你可以在每个矩阵的右侧看到更新的值，标志着矩阵的总数和平均数，如图4所示。
You should see updated values at the right of each metric, indicating both the total number of metrics and the average, as Figure 4 shows.
CwMtx中的矩阵包括向量和方阵，其中向量包括空间向量和四元数。
The matrices in CwMtx include vectors and square matrices, where vectors include space vectors and quaternions.
CwMtx没有内置的随机数生成器，也没有用随机元素填充矩阵的类函数。
CwMtx has no built-in random number generator, and there is no class function that fills a matrix with random elements.
目的研究解决元素为三角模糊数的互补判断矩阵排序问题的新方法。
Aim To study new ranking methods of ranking problem on complementary judgment matrix with triangular fuzzy Numbers.
目的研究解决元素为三角模糊数的互补判断矩阵排序问题的新方法。
Aim To study new ranking methods of ranking problem on complementary judgment matrix with triangular fuzzy Numbers.
应用推荐