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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 30,460
Hi, :) I have some basic knowledge of matrices and vectors. mI understand some of their practical applications in...
Jun5-11 09:26 PM
4 4,233
To simplify this inquiry let us deal with R2. I know that if you have the identity matrix (let that be A), then AA=A....
Jun5-11 04:57 PM
9 2,011
I'm having trouble showing that any normal linear transformation T is the sum of a self-adjoint transformation T1 and...
Jun5-11 03:54 PM
2 1,862
I have encountered a straightforward but strange problem. I know that a discrete time system x(t) in R^6 evolves...
Jun5-11 03:30 PM
0 1,042
I apologize for my lack of knowledge on the topic. I recently started writing programs to solve Project Euler...
Jun5-11 11:44 AM
7 2,150
If I have an R-algebra A where R is a ring, why the center of the endomorphism algebra E_{A}(A) is the algebra of...
Jun5-11 10:26 AM
0 509
how to prove that R(A)=\text{sum of} N(A-\lambda I)? \lambda is nonzero eignevalues of A
Jun5-11 08:08 AM
4 1,078
let B be a matrix formed by deleting n-r rows and n-r columns from A. Why is the singular values of B smaller than...
Jun5-11 07:54 AM
0 523
Let K be a field of characteristic p. Suppose f(x)=(xk+ck-1xk-1+...+c0)(xp-k+.........) in K with 1≤k≤p-1. My...
Jun5-11 04:15 AM
5 896
Hello, today I was thinking the following: it is known that Clifford Algebras provide a general framework to...
Jun4-11 11:31 AM
0 642
Hello, I have a row vector defined as, X=\{x_1,x_2,\ldots,x_L\} I wish to "stack" this vector vertically, a...
Jun3-11 10:07 PM
2 1,653
I've been trying to prove this using rigorous methods, without much success. I've been able to express as a binomial...
Jun3-11 03:39 PM
0 1,551
I am following a proof in the text "Algebras of Linear Transformations" and having problem justifying this line: ... M...
Jun3-11 01:05 PM
3 1,547
Can a sequence of integers from 1 to N be rearranged so that no two neighbors retain their original adjacency?
Jun3-11 12:07 PM
3 1,301
Can somebody please explain to me what is the well-ordering theorem in layman's terms. After looking at the...
Jun2-11 07:16 PM
19 7,817
scratch that. is 5606701775893 a prime number?
Jun1-11 09:10 PM
19 5,577
T is a linear operator from the space of 2 by 2 matrices over the complex plane to the complex plane, that is T:...
May31-11 12:16 PM
2 3,355
I am having trouble understanding the definition of a group C*-algebra, i.e. take a group algebra of a group G and...
May31-11 08:59 AM
11 1,586
How would I go about finding the fraction field of Z?
May31-11 07:53 AM
13 1,123
It is a well known fact that a symmetric bilinear form B on a finite-dimensional vector space V over any field F of...
May31-11 05:47 AM
4 1,686
is there relation between the adjoint (as in conjugate transpose) and the adjoint of a matrix(each entry replaced by...
May31-11 02:10 AM
1 1,765
It's my understanding that algebraic numbers are the roots of polynomials with rational (or equivalently integer)...
May30-11 08:35 PM
2 1,671
Im looking for a method of evaluating large logs without the use of a calculator, such as, log102750. Using...
May30-11 12:33 PM
18 3,177
Hi there, I have 23D subspace, defined by an equation (hyperplane) c1*x1 + ... + c24*x24 = 0; I wonder if there...
May29-11 06:15 PM
6 1,370
for a matrix similar to itself: A=SAS^{-1} A is nonzero and not identity. So is the matrix S must be identity...
May29-11 10:56 AM
3 732
I have a question about mappings that go from a vector space to the dual space, the notation is quite strange. A...
May28-11 01:24 PM
8 2,305
Hi, I know how to calculate matrices determinants but I never figured out why they're so useful in many problems, like...
May28-11 04:33 AM
5 1,195
Could anybody help me find a one line function to calculate the remainder of a number when it is divided by 4 For...
May26-11 09:47 AM
16 2,580
Can a square matrix with a column of all zero's be invertible?
May26-11 09:10 AM
7 2,406
Dear Friends & Colleagues, I have a couple of nagging issues with mathematics I was hoping any one of you would...
May25-11 09:40 PM
1 1,119
Hi, Can anyone help me prove that two commuting matrices can be simultaneously diagonalized? I can prove the case...
May25-11 03:00 PM
McLaren Rulez
6 1,956
Note: I have never formally studied number theory so what I'm about to ask may be either completely trivial or...
May25-11 12:24 PM
7 2,135
According to Wikipedia, the Zeta Riemann Function is defined as follows: \begin{equation} \zeta(z) =...
May25-11 02:55 AM
1 1,957
Is there any method to show that their are infinitley many prime numbers?
May25-11 01:49 AM
6 1,267
Dear Friends & Colleagues, I have a couple of nagging issues with mathematics I was hoping any one of you would...
May25-11 12:36 AM
0 422
I am using Axler's Linear Algebra Done Right as a text for independent study of linear algebra. Axler basically...
May23-11 12:40 PM
4 1,411
Hello everyone, I'm new to PF, so I hope this post is in the correct location. Anyway, does anyone know why one...
May22-11 11:28 AM
2 1,557
In the situation where differences between consecutive squares, (or consecutive cubes, consecutive x^4, etc.) are...
May22-11 04:47 AM
3 2,427
intP(x)Q(x)dx P,Q\inS verify that this is an inner product.
May21-11 11:42 AM
5 1,549
Hi everyone I have a little problem in understanding the trasformation of vectors component when passing to a...
May21-11 11:33 AM
10 1,401

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