1) Kronecker product
矩阵直积
1.
By Kronecker product and the eigenvector of the coefficient matrix, the linear equations set for the hand-eye transformation matrix is derived and the error induced by discarding a block line equation in Nicolas method is overcome.
文中利用矩阵直积和参数矩阵特征向量推导了机器人手眼转换矩阵的线性方程 ,通过最小二乘法得到线性闭解 ,采用Rodrigues公式对所求解的旋转部分进行正交化以消除测量噪声的影响 ,由计算试验证明正交化所引入的误差在绝大多数情况是允许的 ,所求线性解严格满足手眼方程。
2.
The presented methods are based on kronecker product and dual quaternion can solve the rotations and translations simultaneously, and no error propagation.
和现有算法相比,给出的算法分别基于对偶四元数和矩阵直积理论,均可一次计算出标定方程的旋转部分和平移部分,不存在误差的传递问题。
2) Kronecker product of matrix
矩阵的直积
1.
In this paper, we point out the definition and nature in[1] has already been solved and give some nature for kronecker product of matrix.
本文指出文的定义及性质均是矩阵论中已有定义及已知性质,并进一步探讨了矩阵的直积的一些新的性质。
3) matrix direct-product operation
矩阵直积运算
4) matrix perpendicularity
矩阵垂直
1.
The sufficient and necessary condition for matrix perpendicularity and the relationship between the sum of element for matrix Hadamard product and the determinant for this matrix was also found.
找到了矩阵垂直的充要条件,矩阵Hadamard乘积的元素和与此矩阵的行列式的关系。
5) Matrix Straighten
矩阵拉直
6) matrix volume
矩阵体积
1.
The emphase of this paper is to study the defination and properties of matrix volume,it suggested that .
矩阵体积的概念与高维欧氏空间几何学中平行多面体的体积和高维勾股定理相关，也与矩阵代数中向量空间理论有着密切的联系，鉴于此，本文首先对Hilbert空间几何学进行了简要的介绍，在此基础上引入n维欧氏空间，并结合大地测量中的几个具体问题进行了初步的探讨。
2.
Based on the conception of the matrix volume,we presented the definition of the orthogonal degree of the matrices,generalized and extended the determinant method mentioned above.
基于矩阵体积的概念,引入矩阵向量正交度,对病态问题的行列式诊断方法进行了推广和扩展。
补充资料：半直积
半直积
semi-direct product
【补注】A乘以B的半直积通常记作B冈A或B:A.石生明译王杰校半直积[胭顽一面eCt pr仪IuCt;no几ynp“Moe npo“3哪e-““e]，群A乘以群B的 群G=AB，是它的子群A及B的积，其中B是G的正规子群且A门B二{1}.若A也在G中正规，则半直积成为直积(direct Pr以luCt).两个群AB的半直积不是唯一决定的.为构造半直积还应知道A的元素在B上的共扼作用诱导出B的哪些自同构.精确地说，设G二AB是半直积，则对每个元素“任A，对应到自同构:。〔AutB，它是由元素a作共扼: :。(b)=aba一’，b任B.这里，对应a~:。是A~AutB的同态.反之，设A及B是任意群，则对任何同态p:A~AutB有群A乘以群B的唯一半直积，满足:。“印(a)，对任意a‘A.半直积是群B被群A所扩张的特殊情况(见群的扩张(e刀比nsion of agro印));这样的扩张称为分裂的(sPlit).
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条