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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 35,893
Let V be a vector space over a field h and let n be a positive integer. Let f:V -> h^n be a linear map given by f(v)...
Sep1-11 01:30 AM
Josh Swanson
2 1,037
The dihedral group Dn of order 2n has a subgroup of rotations of order n and a subgroup of order 2. Explain why Dn...
Aug31-11 04:24 PM
2 2,699
Hey guys, this question is more or less related to the way Frobenius' theorem is presented in my text. Consider an n -...
Aug31-11 02:19 AM
2 2,046
Im working on understanding Gröbner bases. I've understood how to show existance and uniqueness(of reduced Gröbner...
Aug30-11 06:44 PM
0 1,223
Prove that if a group G has no non-trivial subgroups, G is finite and o(G) is a prime number, where o(G) is the order...
Aug30-11 01:03 PM
5 2,840
There is a Theorem that says FG-Modules are equivalent to group representations: "(1) If \rho is a representation...
Aug30-11 10:04 AM
0 824
Hi everybody, Here is something I've been trying to figure out but to no avail. General problem description:...
Aug30-11 06:26 AM
0 1,190
Suppose I want to decompose A = \left(\begin{array}{cc}4&4\\-3&3\end{array}\right). A = U \Sigma V^T => A^T A = V...
Aug30-11 12:01 AM
18 4,173
This is going to be kind of a long post, and I'm citing the author because it's directly from a textbook, but I'm...
Aug29-11 03:56 PM
3 2,859
Hi there. I started learning about subspaces in linear algebra and I came across a question which i'm unsure how to...
Aug29-11 01:51 PM
14 1,665
Hi! First ever class of Modern Algebra today. I have a question about the well-ordering principle, introduced in...
Aug29-11 01:31 PM
5 2,334
Hi, All: I am trying to see how to classify all symmetric bilinear forms B on R^3 as a V.Space over the reals....
Aug29-11 01:22 PM
1 1,446
the definition of a determinant is not simple at the first sight however we still have extremely simple relation...
Aug29-11 12:06 PM
1 1,134
Hello, I'm trying to find a fast way to solve the matrix equation (A+pI)x=b, where A is a large matrix, I is the...
Aug28-11 08:44 PM
Stephen Tashi
2 1,487
I have to find the number of elements in Aut(Z720) with order 6. Please suggest how to go about it. 1) Aut(Z720)...
Aug28-11 08:06 PM
7 2,432
Hi , I have been thinking of this question for a long time. Can someone give me an advice? There are three known...
Aug28-11 10:48 AM
Stephen Tashi
10 4,060
I have a couple of problems with the conjugate. I have two equations to solve, (conjugate)z=2/z and (conjugate)z=-2/z...
Aug27-11 10:39 AM
5 1,376
Is there any physical significance of the matrix terms such as cofactors and minors? I state that this is used for...
Aug27-11 09:58 AM
Stephen Tashi
1 2,774
Patz, Wilhelm: "Tafel der regelmässigen Kettenbrüche für die Quadratwurzeln aus den natürlichen Zahlen von 1 -...
Aug27-11 03:26 AM
0 1,893
I would like to have this thread dedicated to showing math tricks from all areas of mathematics. Hopefully the title...
Aug26-11 11:00 PM
282 34,047
If you have one pool ball sitting on a table, and you're told to multiply the pool ball by negative one, how can it...
Aug26-11 07:09 AM
10 3,455
If I have a vector: origin = new Vector(x, y) then, I would like to get N sub vectors, each one of the N sub...
Aug26-11 06:37 AM
1 1,620
I am hoping that there may be some frames experts at PhysicsForums that might be able answer the following question: ...
Aug25-11 06:43 PM
0 1,003
Hello. I keep on encountering the need to find the Tensor or Kronecker product of two vectors. Based on the...
Aug25-11 06:41 PM
6 2,555
The Supergolden ratio is the solution of x3=x2+1. \psi = \left({{\sqrt{31}}\over{2\ \times 3^{{{3}\over{2}}}}}...
Aug25-11 05:00 AM
5 4,906
All continuous functions on closed interval form a vector space. The functions in this space are the vectors. However...
Aug24-11 05:24 PM
4 2,605
Do basic operations on vectors, like addition and subtraction change if you change the underlying geometry? For...
Aug24-11 01:47 PM
0 1,191
Hello i have this matrix \in Z mod 7, M = \begin{pmatrix} 0&6\\ 5&0 \end{pmatrix} always modulo 7 in Z. I found...
Aug24-11 06:40 AM
3 1,666
Just as the title says, suppose X is a symmetric manifold and \hat{S}(x) is the linear operator associated to...
Aug24-11 12:38 AM
1 1,425
I've got a question and I really need the answer! Why 10-adics are not a field? And generally, How can you be sure...
Aug24-11 12:30 AM
Citan Uzuki
3 2,206
Hi guys I have a question. What are the physics involved in roulette? I know you have these: -Spin or momentum of...
Aug23-11 05:53 PM
2 2,187
I'm working on an exam that Michael Artin once gave, where one of the questions is basically, Consider the...
Aug23-11 02:12 PM
6 3,112
Let H be a subgroup of a group G. Suppose that if a,b belong to G and there is an x in G such that axa^{-1}=b implies...
Aug23-11 01:58 PM
0 1,026
What is positive and negative eigenspaces? Can you recommend me a referance to know them?
Aug23-11 01:18 PM
2 2,033
Suppose that there is an integer n>1, such that an=a for all elements of some ring. If m is a positive integer and...
Aug23-11 12:43 PM
1 989
I found in page 225 of this article that the endomorphism...
Aug23-11 09:13 AM
0 1,707
Hey, this is my first post, so... Hello everybody! I've been looking into the Collatz conjecture, and like most...
Aug22-11 05:13 PM
2 2,862
I have a quick question regarding matrix equations. Usually, I would look this up but unfortunately I'm away from the...
Aug22-11 09:46 AM
8 1,271
Hello, while dealing with non-homogeneous equations with constant coefficients I met a following problem. I need an...
Aug22-11 09:04 AM
4 2,072
In one of my tutorial problems, I was asked to verify if the following function is a valid inner product <x,y>=...
Aug21-11 03:58 PM
5 2,535

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