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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 36,237
So pretty frequently I encounter questions like a) Are these vectors linearly independent? b) Do they span all...
Y 06:45 PM
3 126
Hi, Are there any rules against multiplying or adding first when using modulo #? The reason I ask is because I'm...
Sep15-14 07:13 PM
3 193
I was wondering what the difference is between the two. Would be nice if someone could explain the difference in...
Sep15-14 04:41 PM
4 175
In Lang's book,page 39-40, he factorizes ##F_{ab}(M)## with respect to the subgroup generated by all elements of type...
Sep15-14 01:54 PM
5 192
So I had a quiz on Wednesday and got the problem wrong but don't know why. The question is: Use elementary row...
Sep14-14 10:45 AM
4 175
Any comments or feedback on this theorem and proof are appreciated, including improvements and past publications. ...
Sep13-14 03:16 AM
3 763
Hi, how can I compute the general solution of a system of linear equations? None-square systems for example. I have...
Sep12-14 03:19 PM
1 256
Let R be a local ring with maximal ideal J. Let M be a finitely generated R-module, and let V=M/JM. Then if...
Sep10-14 06:58 AM
0 196
Hi all, I've been doing some independent study on vector spaces and have moved on to looking at linear operators,...
Sep10-14 03:42 AM
"Don't panic!"
5 330
I was reading the finite element method in engineering by Rao and in the first example he ends up with a matrix that...
Sep8-14 11:53 PM
3 284
Dear all, Please read the text in the attachment. Then...... 1)Explain what is meant by "fix k" and "fixed point...
Sep8-14 12:18 PM
Stephen Tashi
17 2,146
I don't know if this is the correct section for this thread. Anyway, I'm taking a graduate course in General Relavity...
Sep8-14 11:03 AM
19 578
why the metric tensor is the dot product of two basis (co-variants or contra-variants) if it's a tensor then the...
Sep7-14 03:49 PM
6 306
I'm just trying to understand from a linear algebra standpoint how they define dot product from the inner product and...
Sep6-14 07:37 AM
Incnis Mrsi
15 442
Following on from a previous post of mine about linear operators, I'm trying to firm up my understanding of changing...
Sep4-14 04:42 PM
"Don't panic!"
2 254
Hello. Nice to meet you. I have just enrolled. :) I knew how to solve and to find out inverse Matrix by using...
Sep3-14 10:59 AM
2 326
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...
Sep3-14 10:07 AM
Incnis Mrsi
5 506
How can we deform a given Lie algebra? In particular, in the attachment file how can we arrive at the commutation...
Sep3-14 09:58 AM
Incnis Mrsi
2 472
Hey everyone, I've got a question in elementary group theory. Suppose we have a group G, and we want to completely...
Sep3-14 09:09 AM
Incnis Mrsi
6 388
Hi, I'm having a bit of difficulty with the following definition of a linear mapping between two vector spaces: ...
Sep3-14 07:28 AM
Incnis Mrsi
8 606
Hi, I just want to see if I understood this. Since the geometric product is associative and so on we can write for two...
Sep3-14 07:00 AM
3 373
I have a non symmetric matrix AB where A and B are symmetric matrices. How can I find the eigenvectors and eigenvalues...
Sep3-14 06:49 AM
Incnis Mrsi
2 473
(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...
Sep3-14 06:40 AM
Nick O
4 610
I am somewhat confused with the connection between the two groups. In the text I'm reading (An Introduction to...
Sep2-14 11:30 PM
Incnis Mrsi
8 553
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
15 460
hello every body. may i know what is the difference between geometric product and tensor product ?
Aug27-14 07:48 PM
2 386
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
20 844
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
4 559
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
4 482
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
9 688
Hi everybody, do you have an efficient method for build up a vector with random components which is perpendicular...
Aug19-14 10:07 AM
6 496
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
3 576
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
10 667
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!"
2 458
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
3 415
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
2 638
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
1 611
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
1 620
Dear Friends, Please tell me the differences created in ring theory problems when 1.Unity is taken in integral...
Aug14-14 08:27 PM
3 461
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
3 447

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