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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 34,840
Hi PF! Can you please tell me why it is beneficial to use SVD in data processing? My understanding is, given a lot...
T 10:43 PM
2 70
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...
T 01:33 PM
9 247
(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...
T 01:01 PM
Nick O
0 51
Hello, I am trying to understand the slides in the PDF I posted. I am looking particularly at slides 20-24. I am so...
Y 05:57 PM
13 374
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
1 231
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
2 256
In my limited study of abstract Lie groups, I have come across the adjoint representation ##Ad: G \to...
Jul25-14 11:38 AM
center o bass
0 212
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
5 402
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
0 351
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
2 695
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
3 371
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
6 475
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
3 456
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 1,293
Problem 1: Use Gaussian elimination with back substitution to solve the following system. Problem 2: Use the...
Jul19-14 12:38 PM
6 785
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
4 604
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
2 577
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
2 746
Use Gaussian elimination with back substitution to solve the following system: x1+x2+x3=1, x1+2x2+2x3=1,...
Jul17-14 09:34 PM
3 886
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 1,279
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 1,014
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 1,294
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 1,027
The definition (taken from Robert Gilmore's: Lie groups, Lie algebras, and some of their applications): We have...
Jul14-14 01:22 PM
6 1,215
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 5,306
Can you guys give me a concrete example of a completely positive map from M_m → M_n?
Jul3-14 06:26 PM
2 2,250
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 2,319
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 1,807
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 2,041
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 2,496
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 1,939
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 1,900
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 1,784
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 1,752
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 1,833
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 2,023
Please excuse my terminology as I am teaching myself linear algebra. I am attempting to construct a vector which...
Jun18-14 08:52 PM
Simon Bridge
14 2,670
I'm interested in spherical geometry in 4 dimensions. Surely someone has done this, but what is it called? I can't...
Jun17-14 03:08 PM
1 1,729
I've been reading Kreyszig's functional analysis book, and I'm a little confused why he defines the spectral family of...
Jun17-14 02:29 PM
1 1,682
Hello guys, Let ##T: \mathbb{R^2} \to \mathbb{R^2}##. Suppose I have standard basis ##B = \{u_1, u_2\}## and...
Jun17-14 06:08 AM
4 1,912

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