e********e
发帖数: 35 | 1 I've changed my viewpoint and have converted my problem to another one. For
similarities between images there are lots of approaches but accuracy may be
a point. I previously used the idea of simply computing the correlation
coefficients between the two (similar to the matched filter idea, if i am
correct), and it's kind of close. For matrices perhaps can just regard them
as a vector (either by row or by column).
Let me know please if you come to something interesting. thanks. |
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o****o
发帖数: 8077 | 2 Regarding the matrices as a vector will lose spatial information in my case
For
be
them |
|
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l******e
发帖数: 4 | 4 Consider the conjugation action of GL(n) on the space M(n) of n by n matrices. This defines a representation of GL(n) in M(n) whose kernel is just the scalars in GL(n). |
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f******h
发帖数: 104 | 5 Thank you. I have one more question:
how can you prove that the induced map
on regular functions
k[GL(n^2)] --> k[GL(n)] is surjective?
I feel that otherwise the adjoint
representation may be not a closed
immersion.(although the image is closed)
Sorry for my stupidity:)
matrices. This defines a representation of GL(n) in M(n) whose kernel is
just the scalars in GL(n). |
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s**e
发帖数: 1834 | 6 I think the proof is fairly "严格", though might not be as elegant or "clean" as some proof that is more algebraic.
Because when B_0 --> B we have
det(x*I-AB_0) --> det(x*I-AB), so "AB_0 and B_0A have the same eigenvalues" implies "AB and BA have the same eigenvalues".
Btw, when both A and B are degenerate square matrices, the proof only claims
that "AB and BA have the same eigenvalues", but does not claim that "AB and
BA are similar". |
|
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h***5
发帖数: 5 | 8 The problem: f(X)=1/2*||X-B||^2 + V'*max(X, 0)*L.
Here, X and B are matrices with dimension [p, d]. V is a vector with length
p. L is a vector with length d. With known B, V and L, can we get an
analytic solution of X? How to minimize this function over X? |
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l****7
发帖数: 62 | 9 请问：下列这些课对于生物专业转数学master 是否容易？ 谢谢了：
Prob. & Stats I， II
Projective Geometry
Numerical Analysis
Linear Algebra & Matrices
Advanced Calc I， II
Differential Equations II
Complex Analysis
Number Theory
Modern Real Analysis
Exp. Design & Analysis of Variance
|
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G******i
发帖数: 163 | 10 I considered the case of 3x3 matrices.
The nxn case is similar.
(-I+T)^(-1) = =(I+T+...+T^(n-1))/(c -1), where c=a^(n-1) b. |
|
l****7
发帖数: 62 | 11 请问：下列这些课对于生物专业转数学master 是否容易？ 谢谢了：
Prob. & Stats I， II
Projective Geometry
Numerical Analysis
Linear Algebra & Matrices
Advanced Calc I， II
Differential Equations II
Complex Analysis
Number Theory
Modern Real Analysis
Exp. Design & Analysis of Variance |
|
p********e
发帖数: 16048 | 12 都是undergraduate级的
modern real analysis可能对你来说最难
请问：下列这些课对于生物专业转数学master 是否容易？ 谢谢了：
Prob. & Stats I， II
Projective Geometry
Numerical Analysis
Linear Algebra & Matrices
Advanced Calc I， II
Differential Equations II
Complex Analysis
Number Theory
Modern Real Analysis
Exp. Design & Analysis of Variance |
|
d**e
发帖数: 2420 | 13 M=[0,B;C,0]
其中B，C是nxn square matrices.
0--nxn zero matrix
那么M的特征值有什么与B，C有关的表达式吗？
头痛的一个问题，非常感谢。
另外，关于特征值理论有什么好书推荐一下。 |
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l****7
发帖数: 62 | 14 如果我修ＭＡＴＨMASTER 的课， 我需要写电脑程序吗？我打算修下列课：
MA523. Probability and Statistics I, II
MA540. Projective Geometry
MA544. Numerical Analysis.
MA545. Linear Algebra and Matrices.
MA546. Advanced Calculus I,II
MA550. Differential Equations II
MA560. Research Methods of Mathematics.
MA580. Experimental Design and Analysis of Variance
MA623. Statistical Analysis for Forensic Science
MA630. Basic Concepts of Modern Mathematics
MA632. Foundations of Geometry
MA633. Differential Geometry
MA643. Number Theory
MA6 |
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d**e
发帖数: 2420 | 15 Given two positive nxn square matrices A and B with A>=B but A not equal to
B.
Here positive means each entry in A or B is positive.
then whether A's principal eigenvalue is strictly greater than B's?
非常感谢。 |
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G********n
发帖数: 615 | 16 Thank you.
But I need a result for ALL symmetric matrices...
根據隱函數定理 大致上可知在非singular的情況下 解是平滑的 |
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g****t
发帖数: 31659 | 17 就是隐含数定理啊,找本matrxi analysis书就可以看到了.
Thank you.
But I need a result for ALL symmetric matrices...
根據隱函數定理 大致上可知在非singular的情況下 解是平滑的 |
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d**e
发帖数: 2420 | 18 Given two 2x2 matrices
A=diag(a1,a2), B=[a1+b1+p1,-p2;-p1,a2+b2+p2]
Let BI=the inverse of B, that is, B^(-1)
and C=A*BI
Assume all parameters are positive,i.e., a1,a2,b1,b2,p1,p2>0.
If a2,b1,b2,p1,p2 are fixed, then the principal eigenvalue of C is a
function of a1, denoted by, f(a1).
Prove or disprove that function f is monotone with respect to a1.
Any comment or suggestion is welcome. Thanks a lot. |
|
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l*****e
发帖数: 65 | 20 You can write the nxp matrix as the sum of n matrices, each is n by p size,
consisting of one row of B and zeros elsewhere .
Since each such matrix is of rank at most 1, the product with A is of rank
at most 1 too.
QED |
|
l*****e
发帖数: 65 | 21 你要求的矩阵是 Hadamard Matrix， 请见 http://en.wikipedia.org/wiki/Hadamard_matrix。
The order of a Hadamard matrix must be 1, 2, or a multiple of 4.
The most important open question in the theory of Hadamard matrices is that
of existence. The Hadamard conjecture proposes that a Hadamard matrix of
order 4k exists for every positive integer k. |
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i****g
发帖数: 3896 | 22 http://blog.sina.com.cn/s/blog_c24597bf0101b871.html
致谢：I would like to thank Prof. Shing-Tung Yau for suggesting the title of
this article, Prof. William Dunham for information on the history of the
Twin Prime Conjecture, Prof. Liming Ge for biographic information about
Yitang Zhang, Prof. Shiu-Yuen Cheng for pointing out the paper of
Soundararajan cited in this article, Prof. Lo Yang for information about
Chengbiao Pan quoted below, and Prof. Yuan Wang for detailed information on
result... 阅读全帖 |
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q********e
发帖数: 1255 | 23 特征值非负不必正半定，对称性重要。
the classical example:
A=(1 2; 2 5);
B=(1 -1; -1 2); |
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x********i
发帖数: 905 | 24 Sarnak Awarded Wolf Prize
Peter Sarnak has been awarded the 2014 Wolf Prize in Mathematics. A
mathematician of extremely broad spectrum and far-reaching vision, Sarnak
has influenced the development of several mathematical fields, often by
uncovering deep and unsuspected connections. "By his insights and his
readiness to share ideas he has inspired the work of students and fellow
researchers in many areas of mathematics," the Wolf Foundation said. Sarnak
is the Eugene Higgins Professor of Mathem... 阅读全帖 |
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f*******g
发帖数: 55 | 25 Consider a dynamic process { Q[t] } evolving on the set of M-by-M positive
semi-definite matrices. In particular, { Q[t] } follows the recursive
equation:
Q[t+1] = Q[t] - Q[t] a[t] a[t]' Q[t] / (a[t]' (c I + Q[t] ) a[t]) + d I
where:
a[t] is an M-by-1 vector, which can be adjusted;
c and d are fixed positive real numbers; and
I is an M-by-M identity matrix.
Note that by normalization, we can consider a[t] to be a unit vector without
loss of generality.
The "total reduction" at time t
... 阅读全帖 |
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m*******s
发帖数: 3142 | 26 【 以下文字转载自 Chemistry 讨论区 】
发信人: manifolds (流形), 信区: Chemistry
标 题: paper help (转载)
发信站: BBS 未名空间站 (Mon May 19 23:48:03 2014, 美东)
发信人: manifolds (流形), 信区: Biology
标 题: paper help
发信站: BBS 未名空间站 (Mon May 19 23:47:35 2014, 美东)
http://gradworks.umi.com/33/45/3345729.html
Toward the solution of the eigenproblem: Nonsymmetric tridiagonal matrices
by Slemons, Jason, Ph.D., UNIVERSITY OF WASHINGTON
请能下载的同学传到sendspace.com上，给出link, 谢谢！ |
|
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x********i
发帖数: 905 | 28 2014: Alex Kontorovich for From Apollonius to Zaremba: Local-global
phenomena in thin orbits, Bulletin AMS, Vol. 50, 2013, pg. 187-228
2013: John C. Baez and John Huerta, for "The algebra of grand unified
theories". Bulletin Amer. Math. Soc. 47 (3): 483–552. 2010. doi:10.1090/
S0273-0979-10-01294-2.
2012: Persi Diaconis for The Markov chain Monte Carlo revolution,
Bulletin AMS, Vol. 46, 2009, pg. 179–205
2011: David Vogan for The Character Table for E8, Notices of the AMS,
Vol. 5... 阅读全帖 |
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M****o
发帖数: 4860 | 29 这就是个论文奖吧，还不是学术论文，是“expository paper”，跟数学成就没什么关
系。而且就是过去五年之内的文章，所以跟历史上谁得过也没什么太大关系。
“for outstanding expository papers published in the Bulletin of the AMS or
the Notices of the AMS in the past five years.”
比如，06年得奖的是这篇：
2006: Ronald Solomon for A Brief History of the Classification of the Finite
Simple Groups. Bulletin of the AMS, Vol. 38, 2001, No. 3, pg. 315–352.
也就是说，写数学史都可以得奖的。
宗得奖的是这篇：
They are honored for their article "Mysteries in Packing Regular Tetrahedra"
(Notices of the AMS, December ... 阅读全帖 |
|
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o*******w
发帖数: 349 | 31 我在写文章时经常会 struggling 用英语精确表达想表达的东西。写出语言流利优美的
数学论文无疑会使你的论文增色不少, 会使读者和审稿人对你的文章马上刮目相看。我
的经验是在写之前，精读若干好的相关的数学文章，甚至接近达到背诵的程度，要作笔
记，然后再开始写。实际上我是写读同时，在读, 记, 的过程中经常有发现 “这不是
我想表达的吗!”。
但是surprisingly, 好的数学文章（指语言上）并不很多，尤其再考虑要跟本领域相关
就不容易找了，最后只能是矬子里拔大个。
所以我希望大家如果发现有好的数学文章，请不吝推荐。我在这里先破砖引玉，推荐
Joel A. Tropp （他的领域是random matrices）
如果能精读甚至背一下他的若干段落，会收益不浅，甚至终身。他的文章，精确，流畅
, 优美(beautiful)(个人浅见). 你会经常在他的文章中发现你曾经欲述而不达的东西
。稍有遗憾的是他的
领域不完全match我的。 |
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q*****o
发帖数: 438 | 32 业余爱好:
动力系统 (dynamic systems: Arnold diffusion, KAM theorem, renormalization)
黎曼猜想 (the Riemann hypothesis, random matrices, quantum chaology)
请给出群的二维扫描码，多谢。 |
|
l******r
发帖数: 18699 | 33 2015 putnam A6
整个竞赛就数这道题有意思
Let $n$ be a positive integer. Suppose that $A$, $B$, and $M$ are $ntimes n$
matrices with real entries such that $AM = MB$, and such that $A$ and $B$
have the same characteristic polynomial. Prove that $det(A-MX) = det(B-XM)$
for every $ntimes n$ matrix $X$ with real entries. |
|
x********i
发帖数: 905 | 34 http://iccm.mcm.ac.cn/dct/page/1
Plenary Lectures
Group 1
Wei Zhang: RTF and L-functions
Kai-Wen Lan: Cohomology of automorphic bundles
Xinyi Yuan: On Faltings heights of CM abelian varieties
Jing Yu: On Linear Independence of Logarithms
Xuhua He: Cocenter of Hecke algebras
Jiu-Kang Yu: A GAGA theorem for p-adic groups
Jianya Liu: Manin's conjecture for a class of singular cubic
hypersurfaces
Lei Fu: Rigidity of $ell$-adic Sheaves
Si Li: Open-closed topologica... 阅读全帖 |
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i****a
发帖数: 88 | 35 自己顶一下，已经搞定， 其实stiffness和 damping matrices都可以从ANSYS的 .full文件抽取出来，并不一定要用.emat
文件。
另外，ANSYS建模太麻烦， 今天搞定了用Fluent从Icepak里把model的elements&nodes导入ANSYS来提取系统矩阵。现
在原本Icepak里半个小时transient simulation在matlab里用MOR不到一分钟就得到结果了。坏处是现在每天工作量连15
分钟也没有了。 |
|
d**o
发帖数: 79 | 36 Are you working on fluid dynamics? What is the perpose of model order
reduction? In most cases, if we have the stiffness and damping matrices, we
can get the solution directly. |
|
i****a
发帖数: 88 | 37 自己顶一下，已经搞定， 其实stiffness和 damping matrices都可以从ANSYS的 .full文件抽取出来，并不一定要用.emat
文件。
另外，ANSYS建模太麻烦， 今天搞定了用Fluent从Icepak里把model的elements&nodes导入ANSYS来提取系统矩阵。现
在原本Icepak里半个小时transient simulation在matlab里用MOR不到一分钟就得到结果了。坏处是现在每天工作量连15
分钟也没有了。 |
|
d**o
发帖数: 79 | 38 Are you working on fluid dynamics? What is the perpose of model order
reduction? In most cases, if we have the stiffness and damping matrices, we
can get the solution directly. |
|
s********n
发帖数: 52 | 39 1. Mil Med. 2002 Feb;167(2 Suppl):64-5.
Protection against gamma-irradiation with 5-androstenediol.
Whitnall MH, Elliott TB, Landauer MR, Wilhelmsen CL, McKinney L, Kumar KS,
Srinivasan V, Ledney GD, Seed TM.
2. J Biomed Mater Res. 1985 Oct;19(8):941-55.
Bioerodible polyanhydrides as drug-carrier matrices. I: Characterization,
degradation, and release characteristics.
Leong KW, Brott BC, Langer R.
http://www3.interscience.wiley.com/cgi-bin/jissue/109613557
3. J Biomed Mater Res. 1986 Jan;20(1):5 |
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m**********7
发帖数: 13 | 40 Recruiter给我推了一个位置，需要至少Analytical Chemistry的Master或PhD，strong
experience in LC-MS small molecule analysis，Salary is $65-85K. No sponsor.
如果谁感兴趣的话可以发简历给我 [email protected]/* */，我转给Recruiter. 位置在WI.
Please send your resume asap if you are interested since I am not sure how
long this opening could be available.
Description：
Senior Analytical Chemist position
Job Description:
· Perform quantitative method development, validation, and analyses to
support a chemical manufacturing facility
· ... 阅读全帖 |
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S*********g
发帖数: 5298 | 41 Suppose L1 and L2 are two n by n matrice
Outer[Times,L1,L2] gives the write result
Following is a test:
L1={{1,2},{3,4}}; L2={{1,2},{3,4}}
MatrixForm[Outer[Times, L1, L2]] |
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B**h
发帖数: 103 | 42 发信人: beacon (拯之), 信区: Physics
标 题: A Book
发信站: 飘渺水云间 (Thu Sep 9 09:13:15 2004), 转信
A very interesting book, or two thirds of a book,
which follows the tradition of Coleman.
Most QFT books start with QED, after scant discussion of scalar fields.
The beginer is then lost in the Gamma matrices and the subtleties of
gauge theories.
The basics of QFT can actually be illustrated by scalar fields, as
taught in Harvard by Coleman. For many years, people urged Coleman to
publish his lecture notes, with |
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a*******r
发帖数: 7558 | 43 STOKES VECTORS, MUELLER MATRICES, AND POLARIZED SCATTERED-LIGHT
BICKEL WS, BAILEY WM
AMERICAN JOURNAL OF PHYSICS 53 (5): 468-478 1985 |
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h*******r
发帖数: 1083 | 44 Unitary and Hermitian matrices in an external field
Gross, David J.; Newman, Michael J.
Phys. Lett. B 266 (1991), no. 3-4, 291--297
谢谢 |
|
n*********2
发帖数: 3 | 45 最近这段时间关注巴以问题比较多，没怎么关心物理。
但是今天再次看到borland这个名字，决定写点有关他的东西，以完成很久以来的一个
心愿。
这是一个非常深刻非常有趣非常困难的反问题。
我刚开始在物理所做研究生的时候，在图书馆看到过一本书，名字叫reduced density
matrices： Coulson‘s challenge。里面讨论的是这样一个问题。学过量子力学的人
都知道密度矩阵，这个非常本质的概念是landau提出来的，曾经被landau学生列举为
landau十个贡献之一（所谓landau十诫）。对于一个包含有多个子系统的系统而言，我
们除了可以定义和讨论整个系统的密度矩阵之外，还可以定义和讨论单个子系统的密度
矩阵，也就是所谓的约化密度矩阵。定义约化密度矩阵的动机是，如果我们只关系子系
统的物理量的话，我们并不需要知道整个系统的密度矩阵。那包含了过多的冗余信息，
子系统的约化密度矩阵对我们的目的而言足够了。
约化密度矩阵的一个最常见的应用是对全同粒子系统，比如一个原子里的若干电子构成
的系统。对里面的单个电子，我们可以定义单粒子约化密度矩阵；对里面的任何一对电
子，... 阅读全帖 |
|
a*e
发帖数: 431 | 46 不太清楚怎样准确地用数学语言来描述，请大家将就着看看。
俺有一组一共50个对象，想做cluster analysis来分析一下，
可是这组对象俺想交给两组不同的被试来做proximity的区分，
每个组都是99个被试，结果得到个两个50x50的proximity matrices，
数据大概看起来是酱紫，对角线上都是99，也就是被试人数：
矩阵A 矩阵B
A1 A2 A3 . . . A50 B1 B2 B3 . . . B50
A1 99 43 78 B1 99 87 23
A2 43 99 56 B2 87 99 43
A3 78 56 99 B3 23 43 99
. .
. .
A50 B50
两个矩阵都打算用increas |
|
j***o
发帖数: 40 | 47 Thank you for reminding me of posting the second part. I hope viewers can
bring more interesting psychology related articles to this board.
Cattell
we
Matrices
traditional
adaptations
Russia
the |
|
r******n
发帖数: 1 | 48 Rotation matrix solution is not unique. You can use SVD(singular value
decomposition) to find an optimal one. Take correlation matrix R=A*transpost
(B), then do SVD on R: R=U*S*transpose(V) to get orthogonal matrices U and V
. The rotation matrix which minimizes the pairwise distance between A and B
is given by V*transpose(U). More details can be found in Golub's Matrix
Computation. |
|
c*********7
发帖数: 2 | 49 need some self-study books with following areas:
calculus ( fouctions of a single variable; two or more variables; matrices..
...)
series and sequences ( taylors, maclaurin.......)
prob. & stat. ( elementary prob. and stat.; ramdom walks..........)
many many many thx!!! |
|
g******n
发帖数: 339 | 50 各位老大：
我的问题是这样：
Z1,Z2 are both n*1 random vectors with independent(but not identically
distributed) binary componets:
(Z1j, j=1,...,n),(Z2j,j=1,...,n), suppose the mean vector for Z1 and Z2 are
u1 and u2, respectively, hence the variance matrices for Z1 and Z2 are both
diagonal with components: S1:=diag(u1j*(1-u_1j)),j=1,...,n and S2:=diag(u2j*
(1-u2j)),j=1,...,n, respectively.
V1,V2 are constant n*1 vectors.
What is E[(transpose(Z1) * V1)^4]?
What is E[(transpose(Z1)*V1)^2 *(transpose(Z2)*V2)]? |
|
