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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 35,106
There are two "formal" definitions of vectors (and tensors in general) which I've learned. The first is what I...
Y 06:09 PM
15 174
Hi PF! Can you please tell me why it is beneficial to use SVD in data processing? My understanding is, given a lot...
Y 01:54 PM
Stephen Tashi
10 237
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) &...
Y 09:34 AM
0 56
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...
Y 07:58 AM
15 484
While studying Yang-Mills theory, I've come across the statement that there exists a positive-definite inner product...
Jul29-14 01:21 PM
center o bass
0 67
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...
Jul29-14 01:19 PM
center o bass
0 56
In my limited study of abstract Lie groups, I have come across the adjoint representation ##Ad: G \to...
Jul29-14 01:46 AM
1 318
(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...
Jul28-14 01:01 PM
Nick O
0 79
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
13 551
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
1 342
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
2 344
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
5 572
I heard about fast tridiagonal matrix algorithm. I tried to find what is it but I can only find tridiagonal matrix...
Jul23-14 11:58 AM
0 451
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
2 811
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
3 481
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
6 572
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
3 559
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 1,433
Problem 1: Use Gaussian elimination with back substitution to solve the following system. Problem 2: Use the...
Jul19-14 12:38 PM
6 930
Hi, Given several vectors, which may be or not be orthogonal to each other, how to construct a vector perpendicular...
Jul18-14 06:25 PM
4 728
I am working with polytopes that are defined by half-planes in \Re^N. So they are defined by a number of inequalities...
Jul18-14 04:11 PM
2 687
Hi All, Let A,B be algebraic structures and let h A-->B be a bijective homomorphism. Is h an isomorphism? In...
Jul18-14 12:01 PM
2 873
Use Gaussian elimination with back substitution to solve the following system: x1+x2+x3=1, x1+2x2+2x3=1,...
Jul17-14 09:34 PM
3 1,039
Hello, Been a long time lurker, but first time poster. I hope I can be very thorough and descriptive. So, I have...
Jul16-14 04:02 AM
4 1,425
Hi all, Suppose I have a matrix A_{N\times N}. I compute its eigenmodes A V = V \Lambda. V, \Lambda are...
Jul15-14 08:06 PM
1 1,162
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...
Jul14-14 05:44 PM
1 1,451
Hello, Given the complex linear mapping: T(z) = Az + B where A is real and B is complex. However trying to show...
Jul14-14 03:57 PM
3 1,169
The definition (taken from Robert Gilmore's: Lie groups, Lie algebras, and some of their applications): We have...
Jul14-14 01:22 PM
6 1,345
Two groups are isomorphic if they has same number of elements and if they has same number of elements of same order?...
Jul5-14 05:24 PM
12 5,602
Can you guys give me a concrete example of a completely positive map from M_m → M_n?
Jul3-14 06:26 PM
2 2,426
Hi, i was wondering how the following expression can be decomposed: Let A=BC, where B, C are rectangular random...
Jul2-14 04:54 PM
2 2,495
I am trying to diagonalize the following matrix: M = \left( \begin{array}{cccc} 0 & 0 & 0 & a \\ 0 & 0 & -a &...
Jul2-14 12:45 PM
2 1,958
I need help solving for t in the following equation, |P + Vt + A(t^2)/2| = st where P V and A are vectors and s...
Jun30-14 04:45 PM
3 2,221
I've been reading about algebraic geometry lately. I see that a lot of authors use ##V^\vee## to denote the dual space...
Jun29-14 10:45 AM
2 2,671
Hi. In this development (c ∇+ d A)(c ∇+dA)= c^{2} ∇^{2} + d^{2}A^{2} + cd A∇ + cd ∇A (c ∇+ d A)^{2}= c^{2} ∇^{2}...
Jun28-14 11:49 AM
9 2,103
Hi, Can someone explain me the division operation in the picture. First for left division we use (.\ ) not only ( \ )...
Jun26-14 06:22 PM
4 2,051
I was reading in my textbook that the scalar product of two complex vectors is also complex (I assuming this is true...
Jun23-14 08:16 AM
4 1,960
Hello, first of all, sorry if my question is either trivial or imprecise, I'm from the engineering domain :) I...
Jun23-14 06:26 AM
1 1,922
Hey, So I am trying to do a tri-quadratic curve fit (linear regression) in excel. I have successfully completed a...
Jun20-14 11:37 AM
2 1,990
1. Is there a general condition for the existence and uniqueness of solution of a system of simultaneous non-linear...
Jun19-14 07:40 AM
7 2,178

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