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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 30,485
I'm having some confusion with index notation and how it works with contravariance/covariance. ...
Y 02:52 PM
0 76
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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...
Y 01:55 AM
2 111
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
7 213
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
3 162
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
2 108
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
5 167
I've done some more work on my package, adding decompositions of representation powers. It...
Apr17-14 11:59 PM
40 8,316
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
0 125
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
2 165
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
2 171
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
1 222
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 1,090
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
7 257
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
1 180
x1 1 1 0 0 x2 0 0 1 1 x3 = 1 + -1 + 0 + ...
Apr11-14 07:37 AM
2 272
Hi. I am reading a physics text, and in one of the lines it uses the following relation: ...
Apr10-14 10:54 PM
2 258
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
6 297
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
4 276
okay so i'm having some conceptual difficulty given some vector space V (assume finite dimension if needed) ...
Apr9-14 08:07 AM
6 215
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
8 339
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 1,052
##C_0=\{f\in L^p: f(x)\rightarrow 0 ## as ## x\rightarrow infinity\}## This is an interesting subspace because it...
Apr8-14 12:57 PM
10 313
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
0 248
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
12 419
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
3 280
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
1 236
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
2 281
Let's say we randomly select integers to construct a potentially infinite number, for example 3588945.... There is a...
Apr4-14 12:59 PM
2 414
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
1 285
Is there an expression, in general, for the product of two matrix exponentials, for non-commuting matrices? i.e....
Apr1-14 12:36 PM
1 364
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 1,934
Could you explain me: what the difference is between singular value decomposition and eigenvalue problem, when...
Mar28-14 04:48 AM
1 346
Hello, My question is this. Is it possible to prove that there exist an eigenvectors for a symmetric matrix...
Mar27-14 10:28 PM
6 630
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
2 402
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
2 465
In this video, the presenter gets (1, -1)...
Mar25-14 08:23 AM
2 456
Dear All, I need some explanations of properties of tensor and the tensor product on different states;...
Mar25-14 07:19 AM
1 512
If u v = u w, so v = w ?
Mar23-14 03:32 PM
5 584
Hi everyone, I have a general question regarding KPM. Since kronecker product matrices have cartesian tiling, I was...
Mar22-14 01:02 PM
Stephen Tashi
1 422

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