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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 30,539
Hi, I am trying to understand how I find the error in linear regression, and what to do with it. I am using linear...
Jun22-13 11:56 AM
Stephen Tashi
7 583
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
0 356
I am having problems showing the following: ##f## and ##g## are two linearly independent functions in ##E## and...
Jun21-13 02:06 AM
2 609
I have some reason to believe that \det(\textrm{id} + AB) = \det(\textrm{id} + BA) is true even when AB and...
Jun20-13 10:47 PM
2 422
Can someone please explain the below proof in more detail?...
Jun20-13 08:04 AM
12 887
In my work I've encountered equations of the type: (Ax).*(Bx) + Cx = d Where A,B and C are non-unitary square...
Jun18-13 03:28 PM
3 487
I have sets of 2d vectors to be transformed by an augmented matrix A that performs an affine transform. Matrix A can...
Jun18-13 12:24 PM
6 734
I've been studying the proof of the Mazur-Ulam theorem in the pdf linked to at the end of this Wikipedia article. I'm...
Jun17-13 09:59 PM
7 714
Here is the problem: Let f be a real-valued function on the plane such that for every square ABCD in the plane,...
Jun17-13 07:42 PM
7 483
So, I just went through the derivation of the Lie algebra for SO(n). in order to do so, we considered...
Jun17-13 12:15 PM
0 478
Suppose A and B are matrices of the same size, and x is a column vector such that the matrix products Ax and Bx are...
Jun17-13 06:44 AM
2 562
I have some question guys i have four points in the x,y plane in cartesian coordinates. A (Ax,Ay) B(Bx,By) ...
Jun17-13 05:18 AM
5 417
This is slightly applied stuff. Please look at the PDF attached. How do we express the function f(n)ij, found at...
Jun14-13 05:33 PM
14 856
"Let R be a commutative ring. We say that M is an algebra over R, or that M is an R-algebra if M is an R-module that...
Jun13-13 10:53 AM
4 496
I have begun to learn about maximal elements from a linear algebraic perspective (maximal linearly independent subsets...
Jun13-13 06:58 AM
1 406
Hi all, I'm testing out a matrix solving program and while it checks out for 2x2/3x3/4x4 I would like to try it out...
Jun12-13 06:12 AM
Kosh Naranek
1 412
Hi everyone. I'm trying to understand the step where they wrote 1/2 ∏1/(1+p^-3) =1/2 Ʃ(-1)^ord(k)/k^3 How can I...
Jun12-13 03:16 AM
7 533
Was wondering if the only required definition for finite groups is closure (maybe associativity as well). It seems...
Jun12-13 02:13 AM
16 997
For a linear transformation to be invertible, is it a requirement that the domain and codomain be the same vector...
Jun11-13 08:26 AM
3 421
Friedberg proves the following theorem: Let V and W be vector spaces over a common field F, and suppose that V is...
Jun10-13 12:25 PM
1 417
Is there a way without using the algorithm to find A-1 of a square matrix greater than 2x2? The question we are...
Jun9-13 11:04 AM
2 628
For a certain transformation T, it is known that T(x+y) = T(x) + T(y) It is required to determine whether this...
Jun9-13 10:24 AM
5 510
Resource: Linear Algebra (4th Edition) -David C. Lay I understand that there are identities associated with...
Jun9-13 08:32 AM
4 478
How does one show that the set of polynomials is infinite-dimensional? Does one begin by assuming that a finite basis...
Jun9-13 12:39 AM
6 894
Let's say I have some finite subset of vectors in, lets say, ℝ^{5} . If my set has five linearly independent vectors,...
Jun8-13 10:54 PM
6 574
First I'll write what I know: Algebraic number: one of the roots to a polynomial over rational numbers. ...
Jun8-13 09:06 AM
Stephen Tashi
1 530
The definition given is... "Let ##\phi: G \rightarrow H## be a homomorphism with kernel ##K##. The quotient group...
Jun7-13 07:47 PM
7 576
I am reading a number theory text book that states Dirichlet's Approximation Theorem as follows: If α is a real...
Jun4-13 03:31 AM
2 465
Hello, I would like to know if it is possible (and the solution, if known, please!) to extract a 3x3 matrix from a...
Jun3-13 05:45 PM
7 544
Hello, I'd like to make a, probably stupid, question regarding the axioms that define a vetor space. Among them, there...
Jun3-13 10:22 AM
cosmic dust
3 485
Is the following a theorem? yes or no If A and B are non-commuting Hermitian operators (or matrices), there does not...
Jun2-13 12:28 PM
2 732
Are any of the non-division algebras similar to the grassmann algebra?
Jun1-13 05:06 PM
4 673
Hi all! I have no application in mind for the following question but it find it curious to think about: Say that...
May31-13 06:43 PM
1 422
Remember the Newton's binomial theorem which says: (x+y)^n = \sum_{r=0}^n {n \choose r} x^{n-r} y^r where {n...
May31-13 12:13 PM
Stephen Tashi
3 536
Consider ##\vec{a}=\begin{bmatrix} a_1 \\ a_2 \\ a_3 \end{bmatrix}## and ##\vec{b}=\begin{bmatrix} b_1 \\ b_2 \\ b_3...
May30-13 11:53 AM
Ben Niehoff
15 829
Hey, Can somebody help me on this one. I feel out of my depth and have to solve it somehow. I have a variable...
May30-13 06:58 AM
2 443
Using the given information, is it possible to solve the new travel direction of the smiley face? To clarify, I am...
May29-13 06:48 PM
Simon Bridge
6 419
The invertible matrix equation tells us that the following statements are equivalent, for any square matrix A: 1) A...
May29-13 07:39 AM
2 579
Consider the operation of multiplying a vector in ℝ^{n} by an m \times n matrix A. This can be viewed as a linear...
May28-13 03:39 PM
4 476
Here it is for those interested.
May28-13 08:47 AM
0 407

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