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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 35,955
Hi, I just want to see if I understood this. Since the geometric product is associative and so on we can write for two...
Y 05:16 PM
0 85
Dear all, Please read the text in the attachment. Then...... 1)Explain what is meant by "fix k" and "fixed point...
Y 11:50 AM
Stephen Tashi
13 1,888
Hi, I'm having a bit of difficulty with the following definition of a linear mapping between two vector spaces: ...
Aug31-14 04:55 PM
7 377
- - -
Hey everyone, I've got a question in elementary group theory. Suppose we have a group G, and we want to completely...
Aug31-14 07:22 AM
5 202
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...
Aug30-14 06:08 PM
4 315
Hi all, I was asked by someone today to explain the notion of linear independence of a set of vectors and I would...
Aug30-14 05:12 PM
15 257
How can we deform a given Lie algebra? In particular, in the attachment file how can we arrive at the commutation...
Aug28-14 04:49 PM
Greg Bernhardt
1 277
hello every body. may i know what is the difference between geometric product and tensor product ?
Aug27-14 07:48 PM
2 200
Is -(x^-1) = (-x)^-1 true for all nonzero x in any ring, where x^-1 denotes the multiplicative inverse of x?
Aug26-14 02:25 PM
20 550
I've seen it often taught that the combination of two vectors is their graphical sum, but I think that there is a...
Aug23-14 07:18 PM
4 366
I am trying to self study linear algebra. This might seem like a very silly question but what does R subscript 3 mean...
Aug22-14 10:58 AM
4 303
Hi, I have an ordinary least squares setup y = Ac where A is an NxM (N>>M) matrix, c the unknown coefficients and y...
Aug21-14 03:11 PM
9 521
I am somewhat confused with the connection between the two groups. In the text I'm reading (An Introduction to...
Aug21-14 11:00 AM
7 340
Hi everybody, do you have an efficient method for build up a vector with random components which is perpendicular...
Aug19-14 10:07 AM
6 313
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
3 415
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
10 481
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!"
2 300
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
3 254
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
2 461
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
1 443
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
1 452
Dear Friends, Please tell me the differences created in ring theory problems when 1.Unity is taken in integral...
Aug14-14 08:27 PM
3 292
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
1 273
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
3 284
Why do we need fields (Why do we define fields?)for linear algebra?
Aug14-14 12:45 AM
10 360
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
10 422
(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
2 434
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
2 325
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
2 877
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
1 417
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
3 493
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
2 399
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
6 422
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
17 754
While studying Yang-Mills theory, I've come across the statement that there exists a positive-definite inner product...
Aug2-14 11:49 PM
3 505
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 2,000
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
2 435
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
10 687
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
15 885

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