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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 33,813
Theorem: For all a,b,c E Z such that a and b are not both 0, there exist x,y E Z such that ax+by=c <=> gcd(a,b)|c....
Jan9-10 08:56 PM
13 5,319
I have question, can someone please check whether my answer is correct or not: 1)Let \pi_i be representations of a...
Jan9-10 12:40 PM
6 1,253
my question is , given the Group G of symmetries for the equation x^{4} + a^{2}=0 for some 'a' Real valued i...
Jan8-10 04:51 PM
1 737
Two questions: 1. We add the digits of any number. If the sum is divisible by 3, then that number is divisible by...
Jan8-10 05:17 AM
2 5,749
I am trying to show show that there is no homomorphism from Zp1 to Zp2. if p1 and p2 are different prime numbers. ...
Jan7-10 04:57 PM
14 2,776
please explain me associativity for multiplication modulo n
Jan7-10 06:31 AM
1 2,409
I've been trying to prove something that seems obvious but have had no success thus far: say G is a finite group...
Jan7-10 03:55 AM
2 814
HELLO ! THIS IS MY FIRST POST HERE. I spend countless hours playing with numbers and found a general formula to...
Jan6-10 11:06 PM
26 6,047
I'm not sure if this is the best forum for this post, but no single forum seems to be a better fit, and I bet the...
Jan6-10 10:42 PM
0 1,266
Just curious, are there any?
Jan6-10 10:18 PM
8 2,809
Can anyone give me an element in a cyclotomic extension of the rationals that has modulus one but that isn't an...
Jan6-10 07:51 AM
0 747
These are probably a bit stupid, so I hope you don't mind me asking them... 1)what is a fundamental representation?...
Jan6-10 07:26 AM
4 1,031
I've noticed that the order that you do some elementary row operations in for by hand row reduction or gaussian...
Jan5-10 08:54 PM
0 1,622
I'm reviewing my Group theory notes at the moment. I have a few questions. 1)what is the "connected component of...
Jan5-10 08:29 PM
4 1,158
3\times2^{m}+1=n^{2} For some positive integers m and n.
Jan5-10 12:13 PM
3 1,232
I'm reading the book "Numbers" by Ebbinghaus et al. (Springer Verlag); I can't understand what's the main idea about...
Jan5-10 04:16 AM
5 2,902
Hi, I have been struggling with this problem for a while, and I have not found the answer in textbooks or google. ...
Jan4-10 04:57 PM
1 4,039
In the first equation on this page, is there a...
Jan4-10 05:12 AM
1 949
Dear all, does any of you know if there is a routine from popular math libraries (like lapack) which can be used to...
Jan4-10 03:34 AM
0 1,371
I'm working through a proof that every linear operator, A, can be represented by a matrix, A_{ij}. So far I've got ...
Jan2-10 03:43 PM
2 4,940
Help me to solve this equation in algebra More than its width A rectangle has a length of 10 mm long . It has a...
Jan2-10 03:31 AM
1 703
Any pointers and/or help with proving the following would be appreciated For every prime number n, there exist...
Jan1-10 10:04 PM
2 1,793
I'm having trouble grasping what an irreducible representation is. Can someone explain what this is through an example...
Jan1-10 09:04 PM
3 1,422
When we solve for a variable in say two linear equations, by what property we are allowed to add one equation to the...
Jan1-10 08:02 PM
7 2,245
Hi, it is a clear fact that rotations in 3D keep the vectors on the rotation axis unchanged. In 2D only the zero...
Jan1-10 11:39 AM
10 3,252
I still don't fully understand the explicit construction of the tensor product space of two vector spaces, in spite of...
Dec31-09 05:16 PM
12 5,006
Why isn't there a superalgebra having only three basis, c, a,b where c is even and a,b are odd and =a, =-b, =c?
Dec31-09 10:19 AM
1 963
Find all a,b such that a*T(b) + b^2*T(a-1) = b*T(a) + a^2*T(b-1) example solution a = 3, b = 7
Dec30-09 01:05 PM
2 1,582
I know that all the eigenvalues of a real symmetric matrix are real numbers. Now can anyone help out how to prove...
Dec30-09 08:28 AM
4 1,008
I'm reading Algebra (GTM) by Serge Lang and I'm a bit confused about the requirements of theorem 6.3 in chapter 4...
Dec30-09 12:50 AM
0 1,042
Hi, given a complex vector space with a hermitian inner product, how is the cosine of the angle between two vectors...
Dec29-09 05:39 PM
5 2,667
Hi, I was reading the following theorem in the Matrix Computations book by Golub and Van Loan: If V_1 \in...
Dec29-09 08:35 AM
1 2,008
Hi! I have following question. I will explain it with abstract notation although in fact I am working with some...
Dec29-09 04:25 AM
3 1,698
PI(N) = N /{A * LOG(N)^2 +B * LOG(N) + C}. Note: LOG(N) is the common log. This formula works for N up to 10^23. ...
Dec28-09 11:44 PM
5 2,858
On the multiplicity of the eigenvalue Dear friends, Might you tell me any hint on the multiplicity of the max...
Dec28-09 06:10 AM
2 1,239
let U and V be subspaces of Rn. Prove that dim(U+V)=dim U+dim V - dim(U∩V)
Dec28-09 06:09 AM
11 1,020
In the Wolfram Mathworld section on spherical coordinates there's given a list of nine covariant derivatives. The...
Dec28-09 03:55 AM
1 2,916
Edit: Please delete, problem solved.
Dec28-09 01:05 AM
0 855
Hi All, If I is an ideal of J and J is an ideal of R (the ring)... Is it possible that I is not an ideal of R. When...
Dec28-09 12:57 AM
7 1,258
Hi, Can anyone recommend a freely available library in C or C++ that is able to calculate eigenvalues and...
Dec27-09 06:54 PM
3 10,874

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