k******n
发帖数: 35 | 1 I do not think LAPACK is a good choice in your case unless your problem is
really small.
I assume your matrices are dense. Since S and T are positive definite, S^{1/
2} and T^{1/2} can be obtained by Cholesky decomposition. To use LAPACK, K
has to be calculated explicitly. If you only a few singular values, this is
totally not necessary. Consider K as an operator and use ARPACK.
If the problem is small or you need all singular values, LAPACK will be your
choice. However, I would say Matlab will |
|
c*******h
发帖数: 1096 | 2 @Article{polynomial.approx.chebyshev,
author = {V. L. Druskin and L. A. Knizhnerman},
title = {Two polynomial methods of calculating functions of symmetric
matrices},
journal = {USSR Computational Mathematics and Mathematical Physics},
year = {1989},
volume = {29},
number = {6},
pages = {112--121},
}
恳请好心人帮忙下载 |
|
n**f
发帖数: 121 | 3 Assume I have a n*k matrix G where n>k. And I know rank(G) = k. According to
matrix theory G'G has full-rank and its inverse can be calculated. However
when I plug in the data to a numerical software, the software actually
complained that G'G is singular. For my problem, k is between 100 ~ 1000,
and
n is between 500 and 5000.
I manually wrote a C++ Gauss Elimination algorithm to verify that G'G has
rank
of k. But I notice that the Gauss Elimination algorithm would report the
matrix as singular... 阅读全帖 |
|
发帖数: 1 | 4 【 以下文字转载自 Mathematics 讨论区 】
发信人: matrices (), 信区: Mathematics
标 题: 有人能帮忙解矩阵方程吗？非线性的
发信站: BBS 未名空间站 (Wed Jul 20 10:08:15 2016, 美东)
矩阵的entries有十几个，要求必须是整数。变量太多，没法手算。不知道什么软件算
比较方便。有兴趣站内联系。需要报酬请报价。谢谢了。 |
|
x*x
发帖数: 46 | 5
basically ppl use SVD to do pseudoinverse.
1. Let B = pinv(A), where pinv(A) is the pseudoinverse of A, m x n matrix.
i.e., ABA = A
2. SVD (Singual Value Decomposition)
Let A = USV', where U & V are orthogonal matrices (U'U=I) and S is
a diagonal matrix.
3. -1
B = V S U'
so what u need is a SVD algorithm. U can get it from
" target="_blank" class="a2">http://www.geocities.com/xiaomaoxiong2000/lin-alg-cpp.hqx
it's been packed in HQX format. use some tools to unpack it first. |
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z*****n
发帖数: 7639 | 6 Just a reminder:
You need to know this solution applies to only one
dimension of your matrices, and shifts only in
one direction.
circshift() can do n-dimentional shift and in both
directions. |
|
x*z
发帖数: 381 | 7 【 以下文字转载自 Computation 讨论区 】
发信人: xxz (星星), 信区: Computation
标 题: Matlab计算精度请教
发信站: BBS 未名空间站 (Thu Feb 12 00:52:49 2009), 转信
我正在用matlab的lmisolver解线性矩阵不等式，碰到一个问题如下：
我需要求解A(X1,X2)<0, where X1 and X2 are unknown matrices,
所以我用lmisolver已经得到一个数值解X1_0和X2_0，为了验证结果，
我计算矩阵A(X1_0,X2_0)的eigenvalues,发现一些在-3E-6附近，
现在我老板的担心是，这些特征值这么小，可能是由于Matlab的计算误差使得
所有特征值都满足小于0的要求。所以希望我得到一些别的数值解使得A矩阵的
特征值离y轴更远点。
我想请教大家，我老板的担心是多余的吗？难道Matlab连1E-6这种计算精度都达不到？
谢谢。 |
|
L***a
发帖数: 76 | 8
多谢！
The encoder RU-algorithm is attached, and A, B, T, C, D, and E are
sparse
matrices.
My current question is:
How to derive the inverse matrix inv(T) ?
Reference:
Thomas J. Richardson and Rüdiger L. Urbanke, "Efficient Encoding of Low-
Density Parity-Check Codes," IEEE Transactions in Information Theory,
47(2), February 2001 |
|
l***g
发帖数: 1035 | 9 power system is more math than electrical. if you are good at linear algebra
it may be easier.
majority of the problems you would deal with have to do with solving big
matrices fast. |
|
s*********i
发帖数: 107 | 10 【 以下文字转载自 Military 讨论区 】
发信人: evelynlin (插完师妹，一夜没睡), 信区: Military
标 题: zz学生拒绝当千老，流泪流了一夜
发信站: BBS 未名空间站 (Tue Nov 13 16:50:50 2012, 美东)
昨夜无眠，为了一个学生。
五年前，他在清华大学数学系四年级。他可以保送直接攻读博士学位，参加了我们
所的入学考试后，研究室建议我考虑他。面谈后，我同意了。
事情开始得非常顺利，他请我担任他大学毕业论文的导师，我给了他一个解矩阵半
张量积方程的小题目。讨论了几次之后，他就做下去了。他很快进入角色，做了一些小
的结果。他的毕业论文，我修改过。后来他告诉我，得了“优”。我也比较满意，觉得
他赢在了起跑线上。
硕博连读的第一年，他在研究生院上课，接触不多。第二年回所，我很快发现了他
的优点。从素质上说，他数学基本功扎实，和他讨论数学问题是一种享受。一些需要细
想或计算的问题，交给他就好了。少则数小时，多则一、两天，一定会给你一个“Yes
”或“No”的解答。
他在科研上的敏感性也很难得。例如在讨论... 阅读全帖 |
|
h***i
发帖数: 4 | 11 我也来报个到
ID: hlili, PhD. Environ. Sci. Eng. (Post-doc in U.S)
个人邮箱：s*******[email protected]
方向： environmental chemistry, atmospheric chemistry, pollutant transport
in environmental matrices, persistent organic pollutants, environmental
nanotechonology, environmental toxicology, waste water treatment, AOPs, Air
pollution control, hazardous management
曾在以下journals发表文章：
Environmental Science and Technology, Atmospheric Environment, Chemosphere,
Journal of Hazardous Materials, Chemcial Physics Letters, Jou... 阅读全帖 |
|
h***i
发帖数: 4 | 12 我也来报个到
ID: hlili, PhD. Environ. Sci. Eng. (Post-doc in U.S)
个人邮箱：s*******[email protected]
方向： environmental chemistry, atmospheric chemistry, pollutant transport
in environmental matrices, persistent organic pollutants, environmental
nanotechonology, environmental toxicology, waste water treatment, AOPs, Air
pollution control, hazardous management
曾在以下journals发表文章：
Environmental Science and Technology, Atmospheric Environment, Chemosphere,
Journal of Hazardous Materials, Chemcial Physics Letters, Jou... 阅读全帖 |
|
r**********t
发帖数: 247 | 13 【 以下文字转载自 ChemEng 讨论区 】
发信人: refinedheart (Lostemple), 信区: ChemEng
标 题: Postdoc opportunity at UIUC
发信站: BBS 未名空间站 (Wed Sep 21 18:49:26 2011, 美东)
My friend is looking for a Postdoc. He is a very nice guy. this is a good
opportunity.
The Illinois Sustainable Technology Center at University of Illinois Urbana-
Champaign is seeking one full time postdoctoral research associate to
conduct laboratory research, model simulation, and field studies concerning
the enviromental fate and transport of ster... 阅读全帖 |
|
a*******t
发帖数: 867 | 14 来自主题: Environmental版 - 审稿转让 Small journal:International Journal of Environmental Technology and
Management (IJETM).
Ref: IJETM_66906 Article entitled "Anaerobic Cr (VI) Bioaccumulation:
Application to Industrial Wastewater and Soil Matrices in Jordan
如有兴趣，请速联系。 |
|
c*s
发帖数: 2145 | 15 发信人: matrice (迎接十六大，走进新时代), 信区: Chemistry
标 题: [转载]美国统计表明：科研人员引用论文时经常不读原文
发信站: 日月光华 (2002年12月16日12:10:15 星期一), 站内信件
【 以下文字转载自 News 讨论区 】
【 原文由 hitonlee 所发表 】
新华网伦敦１２月１４日电（记者 王艳红）美国科学家的一项统计表明，科研论文后
列出的参考文献，有许多可能是论文作者根本没有读过，是直接从其他论文中抄来的。
据１４日出版的英国《新科学家》杂志报道，这是美国加利福尼亚大学洛杉矶分校
的两名科学家无意中发现的。他们在研究信息在不同网络里的传递方式时，注意到一个
科研论文引用文献数据库里有不少印刷错误，其中有很多错误是完全一样的。这表明，
可能有些科学家并没有读过他们所引用的原始论文，只是照抄其他论文的参考文献。
为了验证这一猜想，分析这种情况有多常见，科学家选取了一篇发表于１９７３年
的、关于二维晶体结构的著名论文。这篇文章被别的论文引用了４３００次，其中有１
９６次引用时存在卷数、页数或年份的错误。理论上讲，可能的错误方式数以 |
|
b**s
发帖数: 589 | 16 1。
A photolabile hydrogel for guided three-dimensional cell growth and migration
Y. LUO AND M. S. SHOICHET
Nature Materials 3, 249; April 2004.
| Abstract | Full Text (HTML/PDF) |
Tissue engineering sees the light
To replace or repair body tissues from cultured cells requires a 'scaffold'
that contains pathways to support and guide cell organization. Such
biochemical channels have already been created in two-dimensional gel matrices
to guide tissue formation. But in this month's Nature Materials |
|
c*s
发帖数: 2145 | 17 hehe, saw her student gave seminar last week
migration
matrices
and
pathways
of |
|
n*****g
发帖数: 35 | 18 The Department of Materials Science and Engineering at University of
Delaware invites applications for one postdoctoral position in Professor
Xinqiao Jia’s laboratory. The successful candidate will work on the
synthesis and characterization of novel biomaterials that closely mimic the
molecular composition, mechanical responsiveness, and nanoscale
organizations of the natural extracellular matrices (ECM). The ideal
candidate will have a PhD in organic chemistry, polymer science and
engineering, |
|
s*******y
发帖数: 558 | 19 我重新把问题说明白一遍吧。
我的问题可以这么说：
I was just wondering if the following claim is true or not:
Any square random matrix with entries independently chosen from
continuous distribution is of full rank.
为此我得到了几个解释。 但是太笨叻， 看不太明白人家的阐述。
发在下面大家评论一下。
我得到的第一个解释是：
Yes, except for a set of measure zero. Equivalently... yes, with
probability 1. Random square matrices span NxN-dimensional Euclidean space.
The inverse image of zero under the determinant function is only a
1-dimensional submanifold.
第二个解释：
The above ex |
|
z*****a
发帖数: 17 | 20 如何用已知的correlation coefficient 产生随机数列，使得数列中的每两个数都服从这
个已知的correlation coefficient? 有人说 decompose correlation coefficeint
matric, then linear transform of random variables? 但是我不清楚如何做，请明白
的大虾多多指点，多谢 |
|
w**a
发帖数: 1024 | 21 a cauchy sequence defined in matric space (X,d)
we know any cauchy sequence is bounded.
But this sequence also has infinite number of elements?
infinite bounded sequence can have NO accumulation point? Thanks. |
|
F******n
发帖数: 160 | 22 Kind of interesting. I'll give a quick shot here - just some quick clues. I'll
also along give my reasonings, which should lead to some rigorous proofs or
dis-proofs. No much rigorous analysis has been conducted, so I may miss things
here. Besides, not sure about your motivation for this problem, so I cannot
determine if the answer gives what you want.
First, some basic corollaries can be established:
1. L1 and L2 must have the same rank (the same number of nonzero diagonal
elements)
2. without |
|
B****n
发帖数: 11290 | 23 If f is continuous but not open mapping, then the image is not necessarily
locally compact. ex: f:[-inf,inf]*[-inf,inf]->L2[-pi,pi] with topology induced
by the matric sqrt(integral(f*g)^2)
Define f(x,y)=y*sin(x*t) then f is continuous but {y*sin(x*t)} is not locally
compact because every closed ball contains a set of infinite orthogonal
functions; hence not every sequence can find convergent subsequence. |
|
B****n
发帖数: 11290 | 24 yes, for matric space, closed set means every convergent sequence converges to
itself. |
|
s*******y
发帖数: 558 | 25 yes, this is obvious.
I am looking for other orthogonal matrices
that are not identity. |
|
b*****e
发帖数: 1 | 26 By definition, rotations preserve length and origin, which means
for all points x and y in the space. |T(x)-T(y)|=|x-y|, where T is
the rotation, and T(0)=0. Easy to see such a rotation is a
linear operation.
Let ' donate transpose of vectors and matrices.
● is a dot product.
Since |T(x)-T(y)|=(T(x)-T(y●(T(x)-T(y))=(x-y) ●x-y), let y=0,
we can get T(x) ●T(x)=x●x. Also, since T is linear, we can
write T(x) as Ax, where A is a n by n matrix. Then we have:
T(x) ●T(x)= T(x)'T(x) =(Ax)'(Ax)=x'A'Ax= |
|
|
O**M
发帖数: 29 | 28 I think maybe Grassmann manifold is related here. maybe you can try that.
(e |
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F******n
发帖数: 160 | 29 Because it is not known if they are in the Euclidean space. |
|
F******n
发帖数: 160 | 30 Thanks very much. I don't really know. |
|
|
F******n
发帖数: 160 | 32 Thanks a lot. I like your answers. I would definitely like to see your
collection of references - that would be great!
feyn |
|
F******n
发帖数: 160 | 33 Thanks very much for your response.
feyn |
|
|
H****h
发帖数: 1037 | 35 要开方一下才成为距离。那样就是我说的R^{n*n}空间上的欧式距离了。 |
|
|
j****j
发帖数: 270 | 37 If matrices A and B are related by X*A=B,
Ap is the orthonomal basis of null(A'), so A'*Ap=0
Bp is the orthonomal basis of null(B'), so B'*Bp=0
Then is there a relation linking Ap and Bp?
Thanks a lot |
|
r****y
发帖数: 1437 | 38 two vectors with same dimension
X = [x11, x12]
Y = [y11, y12]
X*Y' = x11y11 + x12y12
X'*Y = [x11y11 x11y12
x12y11 x12y12]
det(X*Y') ~= 0
det(X'*Y) == 0
if generalizing it, for two matrices, X(N*M), Y(N*M), with N<
does X'*Y tend to be much more singular than Y'*X, or under
what conditions, this statement could be true? |
|
c******s
发帖数: 20 | 39 M.L.Mehta, Random matrices，Elsevier/Academic Press, 2004
依赖于你要做什么，和应用方面。 |
|
A****s
发帖数: 129 | 40 I guess you can apply SVD
Extend X to a n*n matrix by adding rows or columns of 0(not sure if
necessary)
Now X=UHV U,V are orthogonal matrices H are diagonal matrix, rank x=rank h
X'X=V'H'U'UHV=V'HHV rank x'x=rank hh=rank h=rank x |
|
r****y
发帖数: 1437 | 41 square matrices C and A, C is a real symmetric matrix
Now F*F' = (-AC + CA'), where ' is conjugate
F is also square matrix,
The question is: can F be uniquely determined? How?
Thanks a lot. |
|
i*****e
发帖数: 68 | 42 Also, how to define multiplication for multidimensional matrices? |
|
d******e
发帖数: 7844 | 43 来自主题: Mathematics版 - 问两个问题 Suppose that A, B, and AB are normal matrices. Prove that BA is also normal
Prove that every real m × n matrix has a real SVD (i.e. every matrix factor
of
its SVD can be chosen to have real entries). |
|
L***n
发帖数: 6727 | 44 as long as the norm makes the set of matrices a complete banach space,
I don't see any essential difference |
|
G******i
发帖数: 163 | 45 我的思路不是已经写了吗？
问题已化为一个多元微积分问题
Minimize |Yc|^2 for real square matrices Y,
under the constraints tr(Y' Y)=P, |Ya|^2 =z1, |Yb|^2=z2,
标准的解法就是Lagrange multipliers那一套。
至于最后求出来的解会不会有一个很简洁的公式，我一下子看不出来，只能请你自己算
一算了。 |
|
o**a
发帖数: 86 | 46 U is a unitary matrix associated with an euler rotation.
A is a 3x3 matrix.
U.A.U(-1) converts A to another matrix. U(-1) is the inverse of U.
Here I need to treat A as a vector of 9-dimensional space, e.g., the basis
vectors can be matrices with only one nonzero element. An operator Q can be
defined that converts A to another vector just as U.A.U(-1) does. Apparently
Q is a 9x9 matrix.
Is there any simple way of showing Q is a unitary matrix? It seems so by my
brutel calculation on reduced dime |
|
k*******r
发帖数: 16963 | 47 来自主题: Mathematics版 - help A, B are n*n matrices, if AB is invertible, how to prove A and B are
invertible? |
|
f*********y
发帖数: 27 | 48 来自主题: Mathematics版 - help just look at determinant of AB, since A, B are n*n matrices, we have: det(AB
)=det(A)det(B), your book will contain this result. Hence if det(AB) is not
0, then det(A) and det(B) cannot be 0 either, thus A and B are invertible.
Q.E.D. |
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A*****s
发帖数: 13748 | 49 这是啥意思？
我想到了orthogonal matrices |
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o****o
发帖数: 8077 | 50 co-ask. I have the same problem in my work, i.e similarity between matrices |
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