d*****t
发帖数: 7903 | 1 问一个挺初级的实用问题：
如果有一个由7个点span成的6-dim 线形空间，其中5个点可以组成一个subspace S1,
如何快速的找到subspace S2 (基), so that S2 is perpendicular to S1?
线代学得还不到家，遇到实际问题就有点茫然了。
谢谢 |
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f**n
发帖数: 401 | 2 In n-dimensional euclidean space R_n, we have a vector A and a subspace S
that belongs to R_n. What is the maximal angle between A and any vector B in
S?
I have some exposure to linear algebra, but am not sure if the problem is a
well solved problem. Any recommendation on keyword, book, paper or web link
will be highly appreciated.
Thanks. |
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B**r
发帖数: 311 | 3 Tang手下这样的master不少哈
X. Wang and X. Tang, "Random Sampling for Subspace Face Recognition," Int'l
J. Computer Vision (IJCV), vol. 70, no. 1, pp. 91-104, Oct. 2006.
X. Wang and X. Tang, "Hallucinating face by eigentransformation," IEEE Trans
. Systems, Man, and Cybernetics (SMC), Part C, vol. 35, no. 3, pp. 425-434,
Aug. 2005.
X. Wang and X. Tang, "Subspace Analysis Using Random Mixture Models," Proc.
IEEE Conf. Computer Vision and Pattern Recognition (CVPR), vol. 1, pp. 574-
580, Jun. 2005.
X. Wang... 阅读全帖 |
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y***u
发帖数: 101 | 4 For two vectors, simply look at the plane spanned by them
and measure the angle on the plane.
For two d-dim subspaces in a n-dim space, look at their intersection I,
which is a (d-1)-dim subspace. Let K be an (n-d+1)-subspace perpendicular
to I. Draw a (n-d)-sphere in K, centered at the projection of I on K,
and look at the fraction of the sphere bounded by the two subspaces.
If the two subspaces have different dimensions, project one onto another. |
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s*****e
发帖数: 115 | 5 Not so familiar with the Green's function approach, so I cannot comment on that.
However, I believe your conjecture is true for the following reasons:
What you want to prove is equivalent to that if the eigenfunctions are normalized with respect to sup-norm then their L2 norms are always bounded away from zero.
Clearly, this not true for general functions. For example, both exp(-kt) and exp(-k)*exp(kt) (k>0) on [0,1] have L2 norms approaching to zero as k-->+ infinity. On the other hand, one can... 阅读全帖 |
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F******n
发帖数: 160 | 6 In that case, it is not a trivial problem, but it could be done by applying
the incremental SVD algorithm.
This efficient/adaptive algorithm was originally given by a guy (Matthew)
from Mitsubishi research lab. You can easily google that paper.
The main point relevant to the LS regression:
b = (X'X)^(-1) (X'y) (1)
is that, matrix inversion (X'X)^(-1) is essentially an SVD problem. As your
new data come in, you should sort of have an updated X and y, and
consequently an updated X'X. In abov... 阅读全帖 |
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B**r
发帖数: 311 | 7 CUHK有这样的master哈
Dahua Lin, and Xiaoou Tang. Quality-Driven Face Occlusion Detection and
Recovery. Proceedings of IEEE Computer Society Conference on Computer Vision
and Pattern Recognition, 2007 (CVPR 2007).
Zhifeng Li, Dahua Lin, and Xiaoou Tang. Discriminant Mutual Subspace
Learning for Indoor and Outdoor Face Recognition. Proceedings of IEEE
Computer Society Conference on Computer Vision and Pattern Recognition, 2007
(CVPR 2007).
Dahua Lin, Shuicheng Yan, and Xiaoou Tang. Pursuing Informative... 阅读全帖 |
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e****z
发帖数: 119 | 8 俺数学比较差，想请教版上高手这个问题有没有general的solution或者只在特殊情况
下可解：就是一些非线性不等式（比如一些variables的平方和小于一个常数）定义了
一个subspace，然后以一个matrix对这个subspace作线性变换。问题是： 能否
explicitly将线形变换后的subspace表达出来？非常感谢。 |
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j****9
发帖数: 4 | 9 R^N 空间，有一Subspace，由矩阵A表示。A是一3乘3正交矩阵。3个列向量表示
Subspace坐标基。现想求Projection矩阵，把R^N 空间点Project到Subspace上。
谢谢！ |
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s****n
发帖数: 1237 | 10 You can think of the event space, under classical probability theory, the
two kids are distinguishable. The total space = (BB,BG,GB,GG)
P1: You know there's a G, so the subspace is (BG,GB,GG), P(GG) under this
conditional space = 1/3
P2: You see one kid is girl, if this is the first kid, subspace is (GB,GG),
P(GG)=1/2; if it's the 2nd kid, subspace is (BG,GG), P(GG)=1/2. So it's
always 1/2
girls?
and |
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s********n
发帖数: 1540 | 11 =================================
zhu li
media lab
corporate central research
futurewei (huawei) technology
bridgewater, new jersey
phone: 908 541 3546
email: z****[email protected]
---------------------------------
About Me
Zhu Li (Bio, CV) is currently a Senior Staff Researcher and leads the Media
Analytics & Processing (MAP) Group of the Core Networks Research, FutureWei
(Huawei) Technology USA, at Bridgewater, New Jersey. He received his PhD in
Electrical & Computer Engineering from Northwestern Un... 阅读全帖 |
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h**********c
发帖数: 4120 | 12 A nonempty subset W of a vector space V that is closed under addition and
scalar multiplication (and therefore contains the 0-vector of V) is called a
linear subspace of V, or simply a subspace of V, when the ambient space is
unambiguously a vector space.
螨虫是一种没有声音的虫子。但是螨虫在迷走神经上荡着秋千，会发出真气般旋律。 |
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r********e
发帖数: 103 | 13 Note that all second-countable spaces are separable. A metric space is
separable if and only if it is second-countable. The two conditions are
equivalent here.
1) A compact metrizable space is second countable. Its subspaces are second
countable too.
2) A second countable metrisable space is homeomorphic
to a subspace of [0,1]^J, which leads to a metrizable compactification. |
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n*****1
发帖数: 172 | 14 请问linear manifold的具体定义是什么? 我在网上google了一下, 也看了一些书, 好
像有两个不同的定义.
第一个是, given a system of vectors x, y, z,..., a linear manifold spanned
by x, y, z... is the set of all finite linear
combinations ax+by+cz+....
另一个定义是, 假设V是一个vector space, L is a non-empty subset of V, if
there exists a v \in V such that L+v is a
subspace of V, then L is a manifold
这两个定义好像不equivalent吧
另外, 第一个定义说的情况, 和subspace有什么不同呢?
谢谢! |
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i****a
发帖数: 88 | 15 MOR usually works on linear system. Assume you have n = 10k nodes in FEM
model, MOR projects the system
matrices into a subspace with order, say ~ 10. So instead of solving a 10k x
10k dimension ODEs in FEM
software, a system of equations with 10 x 10 dimension matrices would be
much faster to solve. Once you get
the solution on these 30 nodes in the subspace, you can project the results
back to the 10k nodes to get the
actual results.
we |
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i****a
发帖数: 88 | 16 MOR usually works on linear system. Assume you have n = 10k nodes in FEM
model, MOR projects the system
matrices into a subspace with order, say ~ 10. So instead of solving a 10k x
10k dimension ODEs in FEM
software, a system of equations with 10 x 10 dimension matrices would be
much faster to solve. Once you get
the solution on these 30 nodes in the subspace, you can project the results
back to the 10k nodes to get the
actual results.
we |
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q********g
发帖数: 10694 | 17 Sobereva
Department of Chemistry, University of Science and Technology Beijing,
Beijing 100083, China
前言：本文主要介绍过渡态、反应路径的计算方法，并讨论相关问题。由于这类算法极
多，可以互相组合，限于精力不可能面面俱到展开，所以只介绍常用，或者实用价值有
限但有启发性的方法。文中图片来自相关文献，做了一定修改。由于本文作为帖子发布
，文中无法插入复杂公式，故文中尽量将公式转化为文字描述并加以解释，这样必然不
如公式形式严谨，而且过于复杂的公式只能略过，但我想这样做的好处是更易把握方法
的梗概，有兴趣可以进一步阅读原文了解细节。对于Gaussian中可以实现的方法，文中
对其在Gaussian中的使用进行了一些讨论，希望能纠正一些网上流传的误区。虽然绝大
多数人不专门研究计算方法，其中很多方法也不会用到，但多了解一下对开阔思路是很
有好处的。
文中指的“反应”包括构象变化、异构化、单分子反应等任何涉及到过渡态的变化过程
。“反应物”与“产物”泛指这些过程的初态和末态。“优化”若未注明，... 阅读全帖 |
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b***y
发帖数: 14281 | 18 你个例子证明你是文科生, 或者最起码线性代数学的只够文科水平。任何一个vector都
能找到一个坐标系使之成为(1,0,0,0,...). 两个矢量有多少非零分量,区别只在于坐标
系选得好不好而已。单个向量组成的subspace永一远都是一维,跟有多少非零分量无关。 |
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p*****h
发帖数: 120 | 24 请求你们不要再看文学城和大纪元这种不健康消息了，她就是受这种小道消息媒体的影
响走火入魔的：http://bbs.wenxuecity.com/currentevent/608435.html 详情看下面一些网站。自称神或基督的船长Hatonn/Aton乘坐太空飞船绕着地球，发行小道消息刊物Phoenix Journals，宣扬乱七八糟的反科学反文化意见，70年代就被法院责令关停了，令人气愤的是网站www.fourwinds10.net依然开放，把她绕进去，言论和宗教信仰自由并不总是好的。
人生是一次明朗的航行，老看阴谋论之类的阴暗东西，人就变质了。让我们以身作
则，不信谣，不传谣，同在一屋檐下，你们会不自觉地用民运/法轮功那一套言辞影响
她的思维习惯。现代社会一年的媒体轰炸量比人类历史上所有媒体量的总和还多很多，
媒体不受管控，容易让轻信的人受骗。
我觉得是她读的经典人文社科类书太少，对历史科学之类毫无根基，所以才随风倒
，下一个法轮功仍然可能把她套进去。
我会慢慢带她多读有营养的时间沉淀下来的知识分子经典必读书，而不是现在各种
鸟媒体的轰炸。
Do you rea... 阅读全帖 |
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f***y
发帖数: 4447 | 25 http://bbs.netbig.com/thread-2702025-1-2.html
一期9篇研究性文章，1/3是科大的，郭光灿组两篇，潘建伟组一篇
另外在news and views还有一篇点评潘建伟的工作
etters
Experimental investigation of the no-signalling principle in parity–time
symmetric theory using an open quantum system - pp642 - 646
Jian-Shun Tang, Yi-Tao Wang, Shang Yu, De-Yong He, Jin-Shi Xu, Bi-Heng Liu,
Geng Chen, Yong-Nan Sun, Kai Sun, Yong-Jian Han, Chuan-Feng Li & Guang-Can
Guo
doi:10.1038/nphoton.2016.144
The violation of the no-signalling principle — information can be
tr... 阅读全帖 |
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p*******f
发帖数: 530 | 26 来自主题: SanFrancisco版 - 家里有老鼠 We used western exterminator
http://www.west-ext.com/
It took about a week and half:
-Initial inspection finding the possibly where the mouse came in.
- Next, desensitize (putting in traps with peanut butter, not setting the
traps because mouse are very careful).
- After seeing that peanut butter was gone, setting the real traps in attic
and subspace.
- Getting the dead mouse out and filling the holes.
The mouse traps are set to kill and we got although 4 mouses.
I am pretty happy with the servi... 阅读全帖 |
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o*******e
发帖数: 69 | 27 来自主题: SanFrancisco版 - 家里有老鼠 Thank you very much!
One more question, will they clean the attic and subspace for customer, e.g.
mice droppings? we found lots at the attic and want them to clean up for us
, and will they use cements to fill the holes?
And totally it's around $300? including all the services, right?
Thanks again!
attic |
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T**r
发帖数: 7016 | 28 有点科幻的味道，人通过subspace communication和其它人、神交流，这好象是Star
Trek,
Star Gate电视剧里面的情节。没关系，等电信技术发展到可以置入芯片到体内，天人
合一就快实现
了。 |
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j****m
发帖数: 8 | 29 看到有人指出在icmlc 2011会议中同一个作者发表论文达10多篇。本文深知做学术
的不易，觉得在短时间内能在同一个会议上发表10多篇论文，不是造假抄袭，就是粗制
滥造。于是随便找了一篇搜索了一下。发现不如所料，亩产万斤果然是有问题的。
请相关专业人员鉴定是否属于抄袭，以及是否还有其他未发现之处。
抄袭文（以下简称USOM文）
Le Li, Xiaohang Zhang, Zhiwen yu, Zijian Feng, Ruiping Wei, USOM: Mining
and Visualizing Uncertain Data Based on Self-Organizing Maps, Proceedings
of the 2011 International Conference on machine Learning and Cybernetics,
804-809
作者单位：
School of Computer Science and Engineering, South China University of
Technology, Guangzhou, China
... 阅读全帖 |
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g*******d
发帖数: 1467 | 30 ☆─────────────────────────────────────☆
starrycao (subspace) 于 (Fri Sep 14 09:49:43 2007) 提到:
回国不久， 遇到一朋友倾诉。 这也是个剩女， 急了， 为了扩大销路, 海外市场也考
虑了， 上了一个什么国际交友网站， 好像是这个zmyuan.com, 不到一周， 真和一个
美国的老博士联系上了，很快就电话打得火热，很多方面都聊得很投缘， 这女士对博
士很是欣赏，动了些真情， 就盼着他回国见面。
后来她渐渐有些苦恼了， 这博士和她熟悉后， 就每次在电话里都聊好多性方面的事情
， 仿佛他以前说的那么多爱好兴趣都消失了， 就最喜欢聊性的话题， 女士觉得难为
情，每次想叉开话题都不成。
他究竟是喜欢我呢？ 还是只是过于寂寞， 生理上苦闷， 想找个人在电话里释放一下
？该原谅他的寂寞， 继续和他聊下去吗？ 这些问题每天都让她心烦意乱， 想放弃又
做不到。
“你们单身的留美博士都这样吧？是不是都寂寞成这个样子了？”她突然劈头盖脸地问
我。
“还不至于吧。。。”我支支吾吾的回答， 仿佛我自己干过什么 |
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a*****i
发帖数: 4391 | 31
I mean you have to put delay on all the sensors, and targeting system.
How possible it is to target a moving object at .2 light speed? What you see
or scan are the positions those objects *were* at, depending on how far the
object is.
Scenario like in startrek just isn't realistic. Maybe you can do over light
speed voice communications based on "subspace", but WYSINWYG (What You See
Is NOT What You Get). |
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S*********N
发帖数: 6151 | 32
children's space is dense, complete and closed.
however it is a subspace. |
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B******1
发帖数: 9094 | 33 看了 Youtube，搞得我头晕眼花。估计楼主去了一个 Star Trek 里面的亚空间(
subspace)，把时间弄弯了(bent)。中国的三秒钟停顿，到了美国也就半秒都不到了。
和汇率差不多。 |
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r********n
发帖数: 7441 | 34 roughly the number of isolated subspaces formed by the convex combination of
feasible points |
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N***r
发帖数: 2539 | 35 但是现在大型稀疏矩阵的线性方程组的运算，很流行的方法不是Krylov Subspace（比
如说GMRES）那一套？并不需要求逆了吧。 |
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c********e
发帖数: 598 | 36
pca?两个点之间的相似程度和他们的距离相关?? Not always.
PCA subspace is to maximize the retained sample variance, rather than
keeping
similarity. |
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s********w
发帖数: 487 | 37 一年多前的帖子被翻出来了，真不容易
太谢谢你了，讲得很具体
我已经来美国了，现在做的是control system那块
但是感觉我上的课，还有做的方向，和EE的control方向很像。现在基本上上的都是EE
的control的课程，以及应用数学开的optimization的课。还挺担心以后出去了竞争不
过EE的control的高手。所以现在在想尽量往化工的control那块靠拢
现在实验室主要做optimization，以及subspace的system identification的方向。也
不知道这个以后出路如何了... |
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m***i
发帖数: 30 | 38 偶然看到，也没注意发贴时间，呵呵。
你有化工背景，现在主要是补控制方面的东西，这样其实挺好的。
多考虑考虑化工方面的应用就行了。
subspace id对于状态空间模型的辨识来说很有用。
优化也是实际工厂中很需要的。
EE |
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s********w
发帖数: 487 | 39 一年多前的帖子被翻出来了，真不容易
太谢谢你了，讲得很具体
我已经来美国了，现在做的是control system那块
但是感觉我上的课，还有做的方向，和EE的control方向很像。现在基本上上的都是EE
的control的课程，以及应用数学开的optimization的课。还挺担心以后出去了竞争不
过EE的control的高手。所以现在在想尽量往化工的control那块靠拢
现在实验室主要做optimization，以及subspace的system identification的方向。也
不知道这个以后出路如何了... |
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m***i
发帖数: 30 | 40 偶然看到，也没注意发贴时间，呵呵。
你有化工背景，现在主要是补控制方面的东西，这样其实挺好的。
多考虑考虑化工方面的应用就行了。
subspace id对于状态空间模型的辨识来说很有用。
优化也是实际工厂中很需要的。
EE |
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H****h
发帖数: 1037 | 41 利用如下定理可以证明只要A>=B，则A的特征值就不小于对应的B的特征值。
假设A是有限维空间上的Hermitian算子，特征值由大至小排列是a_1, a_2, ... , a_n。
则a_k=\max_{k-dim subspace V}\min_{x\in V}(x,Ax)/(x,x).
add
diagonal |
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h****2
发帖数: 9 | 42 for what vector spaces does the distributive law of subspaces
S intersect ( T+U) = (S intersect T ) + (S intersect U ) hold,
+ here is just ordinary operation, not union or direct sum |
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s******i
发帖数: 7 | 43 I need to translate some course description into Chinese. Pls help:
Linear Algebra:
invariant subspaces,
direct sum decompositions,
canonical forms,
inner product spaces.
Probability and Mathematical Statistics:
central limit theorem, point estimation, hypothesis testing, moment-generating
functions, normal sampling theory, sufficiency, best estimators, maximum
likelihood estimators, confidence intervals, most powerful tests, unbiased
tests, and chi-square tests.
Elasticity Mechanics :
Phenomen |
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l*****i
发帖数: 3929 | 44
I need to translate some course description into Chinese. Pls help:
Linear Algebra:线性代数
invariant subspaces,不变子空间
direct sum decompositions, 直和分解
canonical forms, 规范型
inner product spaces.内积空间
Probability and Mathematical Statistics:概率和数理统计
central limit theorem中心极限定理, point estimation点估计, hypothesis testing
假设检验, moment-generating functions（不知道）, normal sampling theory（不知
道）, sufficiency（不知道）, best estimator, maximum
likelihood estimators, confidence intervals, most powerful tests, unbiased
t |
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I*S
发帖数: 203 | 45 1.5.1. Theorem. If X is a normed space, there is a Banach space Y that
contains X as an everywhere-dense subspace (and such that the norm on X is
the
restriction of the norm on Y). If Y1 is another Banach space with these
properties, the identity mapping on X extends to an isometric isomorphism
from
Y onto Y1.
证明中说X的完备化结果为X~，并且X is an everywhere-dense subset of X~(还不清
楚啥
叫everywhere-dense...)；但是后面又说
We shall show that X~ can be made into a Banach space,
~~~~~~~~~~~~~ |
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H****h
发帖数: 1037 | 46 X/M is not a subspace of X. |
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m*****o
发帖数: 2 | 47 很奇怪书上写的是Kn(n是上标)，而不是k2或者k3之类的，很奇怪有n维直线这种概念么
？还是书上的typo……这本书上很多typo，看得我郁闷死了。
如果真的有n维直线，请教一下大家那样应该如何参数化……
还有n维linear subspace，怎么参数化？
不胜感激！！！ |
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