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1.
文章首先考虑了如下问题:给定矩阵A,B∈Cn×m,求循环矩阵X∈CIRn×n,使得min||AX—B||。给X出了问题具有循环矩阵解的条件和解的一般表达式,若用SE表示上述问题解的集合,文章还考虑了最佳逼近问题:给定X*∈CIRn×n,求X∈SE,使得minX∈SE||X-X*||=||X-X*||,其中||·||表示矩阵的Frobenius范XESE数,证明了问题存在唯一解,给出了其唯一解的一般表达式。  相似文献   

2.
指出矩阵方程Am×nXn× 1=Bm× 1与矩阵方程Am×nXn×s=Bm×s的解之间的关系 ;然后给出矩阵方程Am×nXn×s=Bm×s解的存在性定理并给出求其通解的方法 .  相似文献   

3.
研究了方程AT XA=B的D-对称解及其最佳逼近问题.利用矩阵对的标准相关分解定理给出了矩阵方程AT XA=B在D-1 SRn×n上相容的充分必要条件、解的一般表达式及其最佳逼近表达式.  相似文献   

4.
本文讨论了实矩阵方程X^△AX=A(A为非退化实双对称矩阵,X^△为X的双转置矩阵)的非退化解问题,并给出一般解的形式;同时讨论了实矩阵方程石XAX=A的双对称解问题,并给出了一般解的形式.  相似文献   

5.
给定非负矩阵A,求非负对角矩阵X,使得A+X及其各阶顺序主子阵均具有预先指定的谱半径.给出该问题有解的充分必要条件、解的唯一性及算法  相似文献   

6.
广义逆与矩阵方程的解   总被引:1,自引:0,他引:1  
利用广义逆矩阵求矩阵方程AXB=D(有解时)的通解公式及最小二乘解.  相似文献   

7.
在高等代数的诸多方面,如求逆矩阵的问题、解线性方程组的问题、向量空间中不同基下的坐标关系问题和线性变换下的坐标问题等等,都涉及到了解形如Ax=B或者XA=B矩阵方程的问题.当然,这里提到的矩阵A都是n阶可逆矩阵、那么,当A不可逆,甚至不是方阵的情况又是如何呢?本文将讨论一般形式的矩阵方程AXB=C的解的存在情况解法问\题.  相似文献   

8.
应用分块矩阵的等价标准形,讨论了线性矩阵方程Am×nXn×n=Bm×n有非奇异解的充要条件,并给出了非奇异解的一般表达式,从而推广了文[4]的结论.  相似文献   

9.
利用分块矩阵的性质来研究一般线性方程组解的结构,给出了一般线性方程组AX=b的解存在的充分必要条件为-A21A1-11b1┇br br 1┇bm=0.其中,R(A)=R(A11)=r,A11为A的r×r阶子块,A21为A的(n-r)×r阶子块.同时在方程组有解时给出了此线性方程组的通解.  相似文献   

10.
令A是一个指数为2的幂零矩阵,本文给出了二次矩阵方程AXA=XAX的所有解的求解方法.当A是一个秩为1的幂零矩阵时,详细给出了方程AXA=XAX的所有解.  相似文献   

11.
利用矩阵对的商的奇异值分解研究了线性流形上矩阵方程AXA^T=B双反对称解.  相似文献   

12.
本文给出了矩阵方程AX=B的反问题在半正定矩阵(未必对称)类中有解的充要条件,并在有解时给出其解的表达式。  相似文献   

13.
Problem solving is an important skill in the knowledge economy. Research indicates that the development of problem solving skills works better in the context of instructional approaches centered on real-world problems. But students need scaffolding to be successful in such instruction. In this paper I present a conceptual framework for understanding the effects of scaffolding. First, I discuss the ultimate goal of scaffolding—the transfer of responsibility—and one way that scholars have conceptualized promoting this outcome (fading). Next, I describe an alternative way to conceptualize transfer of responsibility through the lens of distributed cognition and discuss how this lens informs how to promote transfer of responsibility. Then I propose guidelines for the creation of problem solving scaffolds to support transfer of responsibility and discuss them in light of the literature.  相似文献   

14.
In this paper I report on 625 student responses and analyse student perceptions of Problem‐Based Learning during their first semester at university. The data I present outlines the scope of the implementation at six entry‐level units for the years 2007 to 2009 and is followed by a qualitative analysis of student responses. Eight themes are conceptualised as stretching along a continuum with one end point representing an instrumentalist and superficial response and the opposite end representing a professional and more thoughtful response. Despite some tension, this implementation of Problem‐Based Learning into the Science Faculty was, in the main, challenging, time‐consuming and rewarding for the majority of students. Two implications for science education evident as a result of this study are that the general student response to change is more positive if they are informed and supported when a different teaching and learning strategy is introduced and that many students require training and support to become self‐directed learners.  相似文献   

15.
数据结构中递归算法实验教学的探讨   总被引:1,自引:0,他引:1  
邓鹰 《怀化学院学报》2004,23(2):132-134
讨论递归算法实验教学的两个问题 问题Ⅰ :先依据有关数学原理写出数递推等式 ,再根据常系数递推等式编写递归算法 ,从而使学生容易掌握递归算法的设计 问题Ⅱ :引入递归状态树 ,使得递归错综复杂的调用关系变得清晰、明了 ,从而使学生更容易分析递归算法的执行过程  相似文献   

16.
讨论与对合矩阵可交换的反对合矩阵。主。要结果如下:(1)给出了与n阶对合矩阵可交换的反对合矩阵的一种表示;(2)对于2阶对合矩阵A,如果A≠±I(I是单位矩阵)。那么与A可交换的反对合矩阵一共有4个,它们是±玎和±进;(3)对于3阶对合矩阵A,如果A≠±I,那么与A可交换的全体反对合矩阵为±iI和±iA,以及±[iik-i]p^-1,±P[-iik-i]P^-1,±P[ikl1+k^2/l-k]P^-1,P[-ikl-1+k^2/l-k]P^-1其中k是任意复数,l是任意非零复数;当廿(A)=-1时,P是A与diag{1,-1,-1,这一对相似矩阵之间的相似因子;当tr(A)=1时,P是A与diag{-1,1,1}之间的相似因子。  相似文献   

17.
Problem‐based learning (PBL) modified for distance education (PBDiL = Problem‐Based Distance Learning) has been used for teaching energy issues at Uppsala University, Sweden. Collaborative learning in groups of seven to eight students was enabled by computer communication and enhanced the use of Internet. Two different teaching methods have been tried and are compared, both being influenced by methods used in conventional face‐to‐face PBL. The problem presentation was entirely built on pictures, and examination through student reports was successful. A student remark, ‘I study on my own but yet not alone’ shows the importance of social contact.  相似文献   

18.
在翻转矩阵概念的基础上,提出了翻转全对称矩阵,并讨论其性质,获得了一些新的结果,给出了翻转全对称矩阵在特殊情况下的分解,将其化成阶数较低的矩阵,从而可极大地减少翻转全对称矩阵的计算量与存储量.  相似文献   

19.
图的一个极大完全子图称为图的一个团.若图G的每一个块为图G的一个团,则称图G为块图.求图的一个最小团横贯集问题和最大团独立集问题分别称为MCTS问题和MCIS问题.文中给出了块图中求解最小团横贯集和最大团独立集的一个线性时间算法,并证明了块图G中的团横贯数等于团独立数,即τc(G)=αc(G).  相似文献   

20.
Given the fact that ecological issues are global and the fact that a large part of humanity is rooted in the Confucian tradition, it is pertinent to ask what lessons can be learnt from Confucianism, in terms of both ecological education and the current debate in environmental ethics. In this paper I argue that while Confucian ethics cannot, strictly speaking, be said to contain an environmental ethic, its main concepts and ideas do constitute a different level of thinking capable of being exploited as resources for ecological education, if not for solutions to the current environmental crisis. It also has the potential to resolve a dispute in the environmental debate in the West. In particular, I argue that Confucianism is committed to the idea that the environment has a value that, while in a sense connected with humans, is independent of humans. I show that Confucian virtues such as humanity, commitment to harmony, filial piety and so on have positive implications for ecological education.  相似文献   

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