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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 30,407
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
7 527
Was wondering if the only required definition for finite groups is closure (maybe associativity as well). It seems...
Jun12-13 02:13 AM
16 978
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
3 416
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
1 409
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
2 619
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
5 506
Resource: Linear Algebra (4th Edition) -David C. Lay I understand that there are identities associated with...
Jun9-13 08:32 AM
4 476
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
6 878
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
6 560
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
1 523
The definition given is... "Let ##\phi: G \rightarrow H## be a homomorphism with kernel ##K##. The quotient group...
Jun7-13 07:47 PM
7 566
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
2 460
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
7 534
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
3 471
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
2 725
Are any of the non-division algebras similar to the grassmann algebra?
Jun1-13 05:06 PM
4 662
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
1 414
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
3 530
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
15 812
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
2 438
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
6 417
The invertible matrix equation tells us that the following statements are equivalent, for any square matrix A: 1) A...
May29-13 07:39 AM
2 575
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
4 473
Here it is for those interested.
May28-13 08:47 AM
0 401
This is something that I haven't really found much info on. I'm a student attending McGill university, and I have a...
May27-13 09:06 AM
8 856
Anyone have an idea when/where there might be accessible draft of the paper, or want to share any insights beyond the...
May27-13 01:49 AM
1 659
When finding lim(x->1) (1+2ln(x))^(1/(x-1)) = 1^(infinity) I let y = (1+2ln(x))^(1/(x-1)) then ln both sides giving...
May26-13 05:10 AM
1 443
I don't really understand the point in Curvature and Torsion, I am wondering if someone could explain them to me....
May26-13 01:22 AM
5 553
Let A be the set of n \times n matrices. Then the identity element of this set under matrix multiplication is the...
May24-13 11:59 PM
1 472
Hi, I don't get which of the many matrix norms is invariant through a change of basis. I get that the Frobenius...
May24-13 09:35 PM
1 618
So, I know that for a set of vectors to be a basis the set of vectors must be linearly independent and also must be a...
May23-13 11:45 PM
6 574
Hey Guys I am Currently doing my degree in information systems. At the moment the subject is PLC(Processing and...
May22-13 07:45 AM
5 623
Just curious about a certain facet of the vector description of a plane. My query is as to why it is defined as n ...
May21-13 08:34 AM
That Neuron
4 596
Hello everyone! I have a question on whether a system of equations can be classified as linear. I have the...
May19-13 11:05 PM
3 537
Hi everyone, I don't quite understand how tensor products of Hilbert spaces are formed. What I get so far is...
May19-13 12:08 PM
6 891
My linear algebra uses "Kyle Numbers" to compute some kernels. But it does not elaborate on what they are and how they...
May15-13 05:02 PM
3 1,452
after finding out what geometric multiplicity was, I was surprised to notice that in every question I'd done it was...
May15-13 03:23 PM
4 683
Dear all, I'd like to apply principal component analysis (PCA) to hyperspectral data (~1000 bands). The number of...
May13-13 08:58 AM
0 583
Any ideas on this? I googled it and got only answers inolving Excel, C++, etc... A formula for finding the digit sum...
May12-13 08:09 PM
5 4,505
How do we go about finding the transformation that was used to go from one matrix to another ( provided of course that...
May12-13 11:17 AM
4 913

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