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Linear & Abstract Algebra

- Vector spaces and linear transformations. Groups and other algebraic structures along with Number Theory.
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Jan16-12 Greg Bernhardt
Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions...
Feb23-13 09:24 AM
1 35,753
I am somewhat confused with the connection between the two groups. In the text I'm reading (An Introduction to...
Y 10:39 PM
Ben Niehoff
4 148
Z = field of integers . If R is a ring and k is an element of Z, write kR = {kr | r is an element of R}. It is...
Aug19-14 03:23 PM
3 138
Hi everybody, do you have an efficient method for build up a vector with random components which is perpendicular...
Aug19-14 10:07 AM
6 161
Can anyone explain the idea behind Hadlock's proof that there is an Sn for every poly of degree n? Theorem 37 page...
Aug19-14 09:59 AM
3 291
Hello again PF! I had a question on singular value decomposition. My question relates to a pepper I have been...
Aug18-14 11:51 PM
10 351
Hi all, Just doing a bit of personal study on vector spaces and wanted to clear up my understanding on the...
Aug18-14 06:42 AM
"Don't panic!"
2 161
This lemma the book states, I can't make sense of it. Lemma: If a,b\in Z and b > 0, there exist q,r \in Z such that...
Aug16-14 02:11 PM
3 138
How can we deform a given Lie algebra? In particular, in the attachment file how can we arrive at the commutation...
Aug16-14 05:39 AM
0 134
The killing form can be defined as the two-form ##K(X,Y) = \text{Tr} ad(X) \circ ad(Y)## and it has matrix components...
Aug15-14 10:23 AM
Pond Dragon
2 342
I've found this paper: Closed Expressions for Lie Algebra Invariants and Finite Transformations and I've attempted to...
Aug14-14 11:20 PM
Greg Bernhardt
1 321
Hi, 2-forms are defined as du^{j} \wedge du^{k}(v,w) = v^{j}w^{k}-v^{k}w^{j} = \begin{vmatrix} du^{j}(v) &...
Aug14-14 11:20 PM
Greg Bernhardt
1 325
Dear Friends, Please tell me the differences created in ring theory problems when 1.Unity is taken in integral...
Aug14-14 08:27 PM
3 176
I have a non symmetric matrix AB where A and B are symmetric matrices. How can I find the eigenvectors and eigenvalues...
Aug14-14 06:17 PM
1 157
In the US, food products have an ingredient list and a "Nutrition Facts" panel. The ingredient list lists all...
Aug14-14 11:36 AM
Stephen Tashi
3 169
Why do we need fields (Why do we define fields?)for linear algebra?
Aug14-14 12:45 AM
10 227
hey pf! can you help me understand what an adjoint operator is? i've read lots of threads and other sites, but am...
Aug13-14 10:50 PM
10 309
(I don't like the title, since it is a bit misleading. But, I couldn't think of a more descriptive title that fit in...
Aug13-14 01:55 PM
Nick O
2 325
Let e_i be a unit vector with one 1 in the i-th element. Is the following expression has a recursive presentation? ...
Aug13-14 10:43 AM
2 216
I heard about fast tridiagonal matrix algorithm. I tried to find what is it but I can only find tridiagonal matrix...
Aug12-14 05:21 AM
2 760
Hi all, I have been searching around and cannot seem to find an answer. I am doing a past paper, and have the answers...
Aug11-14 03:21 PM
1 296
Quick version: I have a vector field f:\mathbb{R}^n\oplus\mathbb{R}^m \to \mathbb{R}^n of two arguments x \in...
Aug11-14 07:11 AM
3 368
Could anyone help me solve this problem? Let A,B be two subspace of V, a \in A, b \in B. Show that the following...
Aug7-14 06:51 AM
2 279
Hi, Just wondering when using the Euclidean Algorithm to find gcd of 4+7i and 1+3i. Where does 2 and 2+i come from...
Aug7-14 12:11 AM
6 306
Hi, I have an ordinary least squares setup y = Ac where A is an NxM (N>>M) matrix, c the unknown coefficients and y...
Aug4-14 07:00 PM
7 380
There are two "formal" definitions of vectors (and tensors in general) which I've learned. The first is what I...
Aug3-14 06:09 AM
17 595
While studying Yang-Mills theory, I've come across the statement that there exists a positive-definite inner product...
Aug2-14 11:49 PM
3 386
The killing form on a lie algebra is defined as $$B(X,Y) = \text{Tr}ad_X \circ ad_Y$$ where ##ad_X: \mathfrak{g} \to...
Aug2-14 10:34 AM
7 1,885
Hello, my problem is the following: A lasers gives out a bunch of data points which are reflected off a metal...
Aug1-14 01:48 PM
2 313
Hi PF! Can you please tell me why it is beneficial to use SVD in data processing? My understanding is, given a lot...
Jul30-14 01:54 PM
Stephen Tashi
10 544
Hello. I need some help. I am not a math wizard by any means, but I find myself in need of math right now. I have...
Jul30-14 07:58 AM
15 777
In my limited study of abstract Lie groups, I have come across the adjoint representation ##Ad: G \to...
Jul29-14 01:46 AM
1 558
Hello, I am trying to understand the slides in the PDF I posted. I am looking particularly at slides 20-24. I am so...
Jul27-14 05:57 PM
13 847
Hi, all. I'm in desperate need of assistance with a matrix I can't get my head around of. I want to solve a system of...
Jul26-14 04:32 PM
1 585
This should be really easy, but I can't seem to find the answer. What does the symbol ##\ominus## mean in the context...
Jul26-14 06:45 AM
2 577
Hi, I have a rather trivial question but google did not really help me. So far I was always familiar with the fact...
Jul24-14 11:23 PM
5 932
Just one simple doubt here. Can we use different scales on the x and y axes be used for denoting linear...
Jul22-14 06:48 AM
2 1,109
I know it should be absolute zero, but in a scientific calculator, which is an app actually, its value is shown...
Jul21-14 05:34 AM
3 763
Hello, I am going over these slides and I am very confused on a couple parts. First of all on the first slide, I...
Jul20-14 01:19 PM
6 850
Hello everyone! I've been learning some basic group theory (I'm new to the subject). And I had a (hopefully) fairly...
Jul19-14 06:37 PM
3 848
Hi,let: 0->A-> B -> 0 ; A,B Z-modules, be a short exact sequence. It follows A is isomorphic with B. . We...
Jul19-14 03:16 PM
4 1,780

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