矩阵乘积里的元素是通过点乘得到的。
The entries in the matrix product are obtained by taking dot products.
得到的一个矩阵乘积不等式及其逆向不等式。
We firstly obtain an inequality of matrices product and its converse inequality.
我们可以用，矩阵乘法或矩阵乘积的形式来表述这些式子。
And we can reformulate this in terms of matrix multiplication or matrix product.
通过运用在域上任何矩阵都是两个对称矩阵乘积的结论，给出了一种辛矩阵的表示方法。
In this paper, the author gives a kind of expression of symplectic matrices by using the result that any matrix on a field is a product of two symmetric matrices.
讨论了矩阵乘积ab与BA的特征值、特征向量及秩等的关系，并得到了矩阵的奇异值分解。
The relationship between the eigenvalue, eigenvector and the rank of the product of matrices AB and BA is discussed, and the factorization of the singular values of matrix a is obtained.
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.
在数量合成方法的选取上，为了克服传统的风险矩阵方法中乘积效应的缺陷，文章引入了在多属性决策中常用的理想点方法。
For the sake of the limitation of product effect of the Probability-Effect Matrix, the paper adopts the Ideal Point Method which is often used in Multiple Attribute Decision Making.
该算法首先将包含互耦系数信息的信号子空间向量表示为互耦系数矩阵和理想阵列导引向量的乘积。
Firstly, the signal subspace vector including information of mutual coupling coefficients is expressed as product of mutual coupling coefficient matrix and perfect array steering vector.
研究表明，失调光学系统的增广矩阵可用三个基本矩阵的有序乘积表示。
It is shown that the augmented matrix of misaligned complex optical systems can be represented by an ordered product of basic matrices.
分层快速多极算法被用来加速用迭代法求解线性方程组时的矩阵向量乘积的运算。
Multilevel fast multipole method is used to fast calculate the matrix-vector product when we solve the linear system by iterative method.
只要记住：如果你要用一个方阵，乘以一个列向量，当矩阵在左，向量在右的时候乘积才有意义。
It's just something to remember: if you have a square matrix times a column vector, the product that makes sense is with the matrix on the left, and the vector on the right.
两个辛矩阵之和不能保辛，两个辛矩阵的乘积仍是辛矩阵。
The sum of two symplectic matrixes is not symplectic conservation. The product of two symplectic matrixes is symplectic conservation.
根据两幅图像中的平面约束，证明了图像对的基础矩阵和同形矩阵的乘积具有反对称的性质。
According to the planar constraints, we proved that the product of the fundamental matrix and the homography matrix of an image pair is an antisymmetric matrix.
本文剖析了线性代数中伴随矩阵、行向量与列向量的乘积、正交矩阵几个较难掌握的概念，由此引出这些概念的一些基本特征和性质。
This article analyzes a few profound concepts, such as companion matrix, line vector, column rector, orthogonal matrix, and recommend many qualities, which are difficult to grasp for many students.
若直接采用最小二乘估计的公式，因计算过程需要求矩阵的逆及乘积，计算量非常大。
If we use the equation of least square estimator directly, computing amount is often very great because course of computing need calculate the inverse of matrix and multiplication of matrix.
其次，在第二章中，我们讨论了将一个非负矩阵分解成有限多个完全不可分非负阵的乘积的问题。
Secondly, we discuss the problem of decomposing a nonnegative matrix into a product of fully indecomposable nonnegative matrices in chapter 2.
矩阵分解是将一个矩阵分解为比较简单的或具有某种特性的若干矩阵的和或乘积，这是矩阵理论及其应用中常见的方法。
Matrix decomposition is making a complex matrix been equal to sums or products of many matrixes, and these matrixes are simpler or possessing some peculiarities.
利用正规矩阵和乘积可交换矩阵的重要性质 ，给出了亚正定矩阵的三个充分条件以及其合同矩阵的两个分解形式 。
And the classical Courant-Fisher theorem is applied to the complex normal matrix by using a kind of decomposition of complex normal matrices.
通过画笔的变换矩阵与其他的矩阵相乘的乘积更新该画笔的变换矩阵。
Updates the brush's transformation matrix with the product of the brush's transformation matrix multiplied by another matrix.
通过画笔的变换矩阵与其他的矩阵相乘的乘积更新该画笔的变换矩阵。
Updates the brush's transformation matrix with the product of the brush's transformation matrix multiplied by another matrix.
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