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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 35,966
Hello everyone! I am trying to solve a large system of linear equations. The form of the matrix is A = T + F. T is...
Apr3-14 08:35 AM
1 465
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
2 467
Could you explain me: what the difference is between singular value decomposition and eigenvalue problem, when...
Mar28-14 04:48 AM
1 469
Using this coordinate system and writing the relationships: \vec{\rho}\;'=R^{-1}(\phi)\vec{\rho} \begin{bmatrix}...
Jan27-14 09:18 AM
2 470
We have a matrix A4x5 and B2x3 can we remove(-) them A-B Thanks
Feb25-14 11:12 AM
1 471
Hi again, I am trying to get a better grasp of induced maps, and trying to see the results that are used/assumed in...
May25-14 11:21 PM
0 471
Hello Everyone, Pardon me if the following is incoherent. From what I understood of what my professor said, he was...
Jan30-14 05:33 PM
2 474
Hi, I'm reading a book about fluid dynamics and I found some strange product between tensors. It's written like this:...
May21-14 03:38 PM
4 474
I've been introduced to the definition of a generalised eigenspace for a linear operator A of an n-dimensional...
Apr5-14 10:25 AM
2 475
I am reading Dummit and Foote, Chapter 10, Section 10.5, Exact Sequences - Projective, Injective and Flat Modules. ...
May12-14 05:41 AM
Math Amateur
4 477
How can I write proper language for these integrals in MatLab ? Your helps really appreciated. Best, John...
Feb1-14 01:26 AM
Simon Bridge
3 478
Hi, I'v got a problem on Chapter 10 of Georgi's "Lie Algebras in Particle Physics". I want to prove u^i v^j_k...
Jul1-13 06:03 PM
0 479
I've looked at this topic for a while and I have yet to come to any sort of conclusive answer when it comes to...
Feb13-14 02:18 AM
2 479
Let H be a normal subgroup of G. Then factor group G/H is an abelian subgroup. For x, y not in H xHyH=yHxH ...
May22-14 09:59 PM
1 479
Am i correct if I say that Fiedler number surges when percolation is at percolation threshold? Assume a randomly...
Mar8-13 10:44 AM
0 480
I'm trying to understand the category theoretic proof of free groups. I know a bit of group theory but little...
Mar20-14 04:44 AM
James MC
0 480
Is it? Personally, I think it is since the max power on any unknown is 1, no trig function, no product of unknowns...
Oct12-12 02:20 PM
1 481
Hi everyone, I have a square matrix J \in \mathbb{C}^{2n \times 2n}...
Feb27-14 11:57 AM
0 482
Suppose θ: A → B is a homomorphism. And assume S ≤ B. Is it necesarily true that if S is a subgroup, that is not...
Apr27-14 02:54 PM
3 484
It is well known that the approximation error of the SVD is \left\| \textbf{A}-\textbf{A}_{\rm SVD} \right\| = σ_k,...
Jul1-13 04:14 AM
0 485
Hi Guys, I have just started studying about this field. Can you give me some ideas about some best eigen value...
Jun22-13 08:50 PM
1 485
Is there an expression, in general, for the product of two matrix exponentials, for non-commuting matrices? i.e....
Apr1-14 12:36 PM
1 485
Dear All: For a line structure(say a very long atomic chain) and a closed loop structure( connect the head and tail...
Oct31-13 10:59 PM
0 486
Hi, All: I have seen Orthogonal groups defined in relation to a pair (V,q) , where V is a vector space , and q...
Jun10-11 09:11 PM
0 487
Hi there. I would like to learn more, if any, on interesting applications of Euclidean rings both in mathematics,...
Jun23-13 04:33 PM
0 488
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
10 488
Hi, all: Say we have a bare-bones Vector Space v, i.e., V has only the basic vector space layout; no...
Apr27-11 04:47 PM
1 489
I'd like to figure out why f(x) = x^n - r e^{i \theta} = \prod_{j = 0}^{n - 1} ( x - r^{1/n} e^{i \theta / n} e^{2...
Feb9-14 03:33 PM
2 492
Hi, I have found an encryption algorithm named ECKS-PS (published in a paper named 'efficient conjunctive keyword...
Apr10-13 03:13 AM
0 493
How I do for calculate the solid angle formed by 3 vectors like: ?
Feb18-14 11:15 AM
2 494
Hi all, Note: The text below is the motivation for my question. To jump to the question immediately, please skip to...
Jul26-13 07:14 PM
0 495
I imagine a matrix group, with multiplication as the composition rule, to always possess the quality of having centre...
Feb20-14 01:57 PM
3 495
Is it possible for a variable to exit the basis and after a couple of iterations, enter it again? Are there any...
Jun9-11 09:31 AM
0 496
Here it is for those interested.
May28-13 08:47 AM
0 496
There are lots of examples of numbers where "is it a rational number" has been an open question for a while before...
Jun21-13 01:54 PM
0 496
The two properties every linear transformation T: V -> W has to satisfy is T(u + v) = T(u) + T(v), for u,v in V (i)...
Feb17-14 04:01 PM
4 496
The Fourier series can be used to represent an arbitrary function within the interval from - π to + π even though...
Jun28-13 03:39 PM
1 498
is it true that \frac{1}{g_{ab}}=g^{ba}? I am a bit confused by the index notation. I especially wonder about the...
Apr6-14 06:12 PM
3 498
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
3 499
If I have two square nonnegative primitive matrices where the Perron-Frobenius Theorem applies how would I calculate...
Jul4-13 09:01 PM
Simon Bridge
2 500

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