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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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Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions...
Feb23-13 09:24 AM
1 30,530
We have that A and B belong to different representations of the same Lie Group. The representations have the same...
Y 08:33 PM
3 134
Just by looking at the cayley table of a group and looking at its subgroups, is their a theorem or something which...
Y 01:59 PM
0 57
In "A Student's Guide to Vectors and Tensors" by Daniel Fleisch, I read that the covariant metric tensor gij=ei°ei...
Y 12:24 PM
1 94
Here's the claim: Assume that A and B are both symmetric matrices of the same size. Also assume that at least other...
Apr22-14 07:01 PM
8 132
I was wondering if universal algebra had any applications in physics. I've done some searches and people have...
Apr22-14 06:00 AM
2 165
##C_0=\{f\in L^p: f(x)\rightarrow 0 ## as ## x\rightarrow infinity\}## This is an interesting subspace because it...
Apr21-14 05:32 PM
14 394
I'm having some confusion with index notation and how it works with contravariance/covariance. ...
Apr21-14 10:45 AM
1 145
Hi, (hope it doesn't seem so weird), I'm looking for a general expanded form of (x+y+z)^{k}, k\in N k=1: x+y+z...
Apr20-14 01:55 AM
2 154
I am a bit dense when it comes to linear algebra for some reason. I am reviewing math to prepare for a physics grad...
Apr19-14 06:38 PM
7 248
I'm hoping that you can help me settle an argument. For a matrix \textbf{M} with elements m_{ij}, is there any...
Apr18-14 11:11 AM
3 195
The position vector ##\vec{r}## in cartesian coordinates is: ##\vec{r} = x \hat{x} + y \hat{y}##, in polar coordinates...
Apr18-14 10:20 AM
2 144
I'm interested in the use/application of the trace of a square matrix? I am trying to get an intuitive feel for what...
Apr18-14 10:20 AM
5 201
I've done some more work on my package, adding decompositions of representation powers. It...
Apr17-14 11:59 PM
40 8,413
Hi, I'm new to this subject and wondering if anything is known specifically on the zero-th Gaussian periods of...
Apr17-14 08:29 PM
0 158
Hi All: We know that the quotient ## \mathbb Z /2\mathbb Z ## ~ ## \mathbb Z/2 ## . Is there a nice way of...
Apr16-14 09:30 PM
2 197
Hi, I am trying to follow an introductory problem in my book for which no solutions are provided and have got...
Apr16-14 06:48 AM
2 207
I am wanting to find a good proof of the Lindemann-Weierstrass Theorem. Most importantly I need the part that...
Apr14-14 11:42 AM
1 256
I have a uniform grid of data in spherical coordinates. e.g. theta = 0, 1, 2, ... 180 and phi = 0, 1, 2, ... 359 which...
Apr14-14 07:12 AM
3 1,127
I'm looking for a proof of a validity of the inequation: (n-1)\sum_{i=1}^{n}x_{i}^{2}\neq...
Apr13-14 11:00 PM
Simon Bridge
7 290
Given a vector ##\vec{r} = x \hat{x} + y \hat{y}## is possbile to write it as ##\vec{r} = r \hat{r}## being ##r =...
Apr13-14 09:54 AM
1 216
x1 1 1 0 0 x2 0 0 1 1 x3 = 1 + -1 + 0 + ...
Apr11-14 07:37 AM
2 307
Hi. I am reading a physics text, and in one of the lines it uses the following relation: ...
Apr10-14 10:54 PM
2 291
Hi guys, I have this general question. If we are asked to show that the direct sum of ##U+W=V##where ##U## and...
Apr10-14 09:55 AM
6 334
say X = (AB) (B-1 C) B-1 = B inverse (B B-1 = B-1 B = I) then can i write X = AC? just having a brain fart...
Apr9-14 08:11 AM
4 309
okay so i'm having some conceptual difficulty given some vector space V (assume finite dimension if needed) ...
Apr9-14 08:07 AM
6 247
Hi, i'm reading up on linear algebra and I'm wondering if the remark after a theorem I'm reading here is complete. The...
Apr8-14 09:24 PM
8 379
hey pf! so my question is how cramer's rule makes sense from a geometric perspective. i'm reading the following...
Apr8-14 07:26 PM
3 1,088
Hello, I have a 2\times 2 real matrix M such that: M=A^T \Sigma A, where the matrix \Sigma is symmetric positive...
Apr8-14 02:45 AM
0 280
Not sure if this is the right subforum. This is technically a signal processing question, but it edges on proving...
Apr7-14 11:24 AM
12 467
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
3 314
In the following 0/1 matrix I'm trying to identify every largest submatrices formed by 1's as shown in the picture. ...
Apr6-14 12:20 PM
1 268
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
2 312
Let's say we randomly select integers to construct a potentially infinite number, for example 3588945.... There is a...
Apr4-14 12:59 PM
2 448
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
1 323
Is there an expression, in general, for the product of two matrix exponentials, for non-commuting matrices? i.e....
Apr1-14 12:36 PM
1 395
I was trying to solve the following equation: \bigwedge\limits_{j=1}^{k}\begin{bmatrix} a_{1,j}\\ a_{2,j}\\ ...
Mar28-14 08:33 AM
13 1,976
Could you explain me: what the difference is between singular value decomposition and eigenvalue problem, when...
Mar28-14 04:48 AM
1 379
Hello, My question is this. Is it possible to prove that there exist an eigenvectors for a symmetric matrix...
Mar27-14 10:28 PM
6 669
Hi, Could anyone give me a proof for the following theorem? Theorem : Ax=0 has a non-trivial solution iff det(A)=0...
Mar27-14 06:47 AM
2 436
The interpretation of the vector product is the area of the parallelogram with sides made up of a and b and the scalar...
Mar26-14 09:48 PM
2 499

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