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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 36,204
I found this problem on the MIT OpenCourseWare website, but a solution was not given. I tried it out, so I was...
Jul31-05 01:20 PM
4 1,506
Does anyone know a good website, or have a PDF file that gives a good introduction to congruencies? I can't seem to...
Aug6-05 04:22 PM
1 1,295
I just have one question about the proof. Why does (p-1)!a^{p-1}=(p-1)!\pmod{p}? It seems like it would be true if...
Sep10-05 08:54 PM
5 9,356
Find the general solution to the following system of equations and indicate which variables are free and which are...
Sep24-12 09:03 PM
Simon Bridge
1 844
Hello, So I'm trying to understand the construction of the tensor product of 2 vector spaces as stated in the...
Dec18-08 05:05 PM
1 931
I have these questions on my studyguide and I know both of them are false. I just don't have a good counterexample or...
Mar17-12 04:38 PM
5 1,345
How do I show that for any vectors u,v, and w in a vector space V, the set of the vectors {u-v, v-w, w-u} is a...
Mar19-12 11:39 AM
6 2,994
Hi When we have f(n) \in o(g(n)) and g(n) \in O(H(n)) Can I proove that h(n)-f(n) \in o(g(n))? Obviously I...
Sep9-12 05:48 PM
3 1,713
Does anyone know an algorithm for computing kronecker products of two matrices? It's probably not that hard, but I...
Apr20-12 09:59 AM
2 1,835, but haven't got any responses, so I thought I'd try here] Iím building a model in a 3D...
Mar10-14 02:44 PM
2 945
Does an inverse exist for every quaternion under multiplication??
Feb24-08 02:36 AM
1 3,046
Im having trouble under stand the relationships between determinats, span, basis. Given a 3x3 matrix on R3 vector...
May8-12 04:37 PM
3 1,123
Are there any numbers that is not considered to be a subset of a complex number subset of a + bi Where a and b...
Jan9-12 07:55 PM
3 1,797
Using vectors to Go from one point to another restricts us with merely orthogonal mathematics that pertain to our...
Feb8-12 03:02 PM
0 1,159
Hello all, I have a MATLAB Ax=b problem where A is a matrix generated from the eigenvalues/ vectors of another...
Feb7-06 01:32 PM
0 2,870
Dear all, I want to find functional relationship between two datas set.How to find,it relation is...
May9-07 01:10 PM
5 1,118
1. The problem statement, all variables and given/known data How do I show that the cp is p(x)=x^n, dimA=n? 2....
Oct8-09 07:10 AM
7 5,157
A long time ago I took a number theory course and really enjoyed it. At one point we were shown the proof for the...
Sep28-10 09:19 PM
1 2,834
Hello, I was thinking about how to predict the order of an element a*b if the orders of a and b are known where a...
Mar1-09 04:59 AM
Citan Uzuki
2 1,642
Multiplication is defined as repeated addition. 3x5 = 5+5+5 How do we define 10/2?
Oct15-03 12:05 AM
6 6,774
Hi So I'm looking at presentations. I think that I understand that the group that generates <a,b|a^2,b^2> is Z/2 x...
Jan23-10 10:15 AM
1 832
There are 4 vectors, all the same length - |v1| = |v2| = |v3| = |v4| = 1 I need to find greatest possible value for:...
Apr2-11 10:37 AM
0 529
I'm trying to find the number of different non-singular matrices (nxn) over a finite field (order q). Any help would...
Nov30-08 05:31 PM
2 5,886
Hi everybody, I am having an extremely hard time understanding a specific relationship that originates from the...
Nov7-10 03:20 PM
2 2,284
Hi, I read that the general form of an inner product on \mathbf{C}^n is: \langle \vec{x} , \vec{y} \rangle =...
Nov22-10 08:38 AM
3 2,214
This isn't a homework problem, but something I was kicking around. Thus far it has worked for the first 20 primes I...
Jan29-10 10:28 AM
11 2,313
Given a 4x4 non-Hermitian matrix, is there any method I can use to prove the eigenvalues are real, aside from actually...
Jul15-09 08:51 AM
2 1,442
Prove that the sum of any two consecutive odd prime numbers can always be written as the product of three integers,...
Nov12-10 08:43 PM
6 2,502
Hi. I might just have something here. Please let me know if you have any questions or comments. Thanks. Andy Lee....
Jan15-10 08:27 AM
Andy Lee
48 9,025
Yes, the method uses a sieve, but the problem of endpoints has been overcome. Let S=(..., -5, -3, -1, 1, 3, 5,...
Feb3-10 09:51 PM
20 3,535
Hi, I was just hoping for some suggestions for a good book to learn abstract algebra with. Specifically, I'd like a...
Jul20-04 05:42 PM
7 2,765
Let B be a basis for a vector space V (with an uncountable dimension!) over a field F, and let K be a linearly...
Nov27-07 12:15 AM
9 2,057
I am reading "The linear algebra a beginning graduate student ought to know" by Golan, and I encountered a puzzling...
Jun10-08 07:59 PM
7 6,219
My recent interest in using transfinite induction in linear algebra has led me to pose a new question. (I will use c...
Nov24-07 02:48 PM
7 2,161
I can't seem to figure this one out: Question: Let D be a nonempty subset of a vector space V over a field F. Let...
Dec9-07 06:55 PM
2 2,616
Let V be an inner product space whose inner product g is not positive-definite but simply nondegenerate (Minkowski...
Dec23-07 04:51 PM
4 2,818
Feb7-05 08:09 PM
0 1,344
I need some help with understanding the basics of Lie algebra theory. I suspect my problems are due to a fundamental...
Jan4-12 04:57 AM
1 1,148
hi, im having a bit of trouble understanding how to formulate rhis problem, can someone please help me? the...
May10-04 04:56 PM
3 1,214
hi, Could someone please show me how these are a linear transformation please: 1) T(s u + r V) ...
May17-04 05:05 AM
2 2,355

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