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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 36,260
Find the characteristic and minimal polynomials of A=] (3x3 matrix) So when I work out my...
Feb16-05 11:25 AM
4 7,505
It is true that if a norm satisfies the parallelogram equality then it must come from an inner product right (i.e. < ,...
Dec21-04 02:11 PM
matt grime
2 7,498
I am trying to find a way to generate solutions to 5b^2*c^2 = 4a^2(b^2+c^2) Can anyone offer some insight? I...
Dec13-12 06:26 AM
55 7,483
I am a member of the Dozenal Society of Great Britain ( ) . We maintain that base twelve is...
Jan14-10 03:17 PM
34 7,467
Can someone guide me through the proof (or point me to where I can find the proof) that the group of rational numbers...
Apr29-04 12:46 PM
7 7,456
About 20 years ago I caught an article about a graduate student who had found an algoritm which would return the n-th...
Sep27-06 07:55 PM
14 7,448
I'm working on a skeletal animation system, and I want to interpolate the rotations between frames. The rotations are...
Jan27-05 04:42 PM
2 7,424
Can isomorphism of matrix groups \phi: G_1 \rightarrow G_2 always be expressed by \phi(M) = S M S^{-1}?
Jul25-08 03:43 AM
16 7,423
Hi, This is the problem: Lorraine has $7.70 in dimes and quarters. If the number of quarters is two more than twice...
Apr30-05 10:30 PM
2 7,406
How to find detA if A is 4x4 matrix or more than 4x4.
Oct29-10 12:01 AM
7 7,399
I have to prove that if ab is divisible by the prime p, and a is not divisible by p, then b is divisible by p. In...
Aug6-04 08:10 AM
9 7,391
Investigating the Diophantine equation q = \frac{n^2+1}{p}} where {p} is a prime number, n,q are integers per...
May18-05 07:56 AM
5 7,369
hello all after doing a bit of research on the riemann hypothesis I came along this paragraph, in which I dont...
Dec10-10 01:37 PM
16 7,357
I mean, according to my knowledge, Bertrand's postulate has already been proved, I've already read and understood one,...
Apr30-10 04:11 AM
20 7,345
I am reading (theorem 2.14) from a textbook, and don't understand how g = Tf and (#1) line of reasoning. The theorem...
Oct19-09 11:08 AM
9 7,336
Hi, I have been searching the web for this subject to see if the formula I stumbled on is out there. This site...
Jun13-08 05:58 AM
jim mcnamara
1 7,327
I've done 3 of my 5 problems, which took me 2 days and over 30-50 pieces of scrap paper. I'm serious, I didn't even...
Oct5-05 12:16 AM
6 7,322
Q: If A is an m x n matrix and rank A = m, show that m <= n. I know that by definition if A is m x n, then rank A...
Jul13-05 10:46 PM
9 7,321
Sep30-11 05:47 PM
19 7,311
Cantor's diagonal slash has been used to argue that the infinity of reals is uncountable, whereas the infinity of...
Mar7-05 05:23 AM
44 7,306
Hi I don't understand why only a matrix full of zero has a rank = 0. "the rank of a matrix A is the number of...
Mar27-11 12:32 PM
5 7,296
Greetings, I just stumbled upon this site and thought someone might be able to help me. How many elements of order 5...
Oct6-04 11:22 AM
2 7,295
I'm looking at the exercises of Hungerfod's Algebra. Some looks easy but it seems the proofs are not so obvious....
Nov11-09 12:27 AM
Spartan Math
4 7,285
Hello, can anyone tell me if I understand this right? :rolleyes: I have a t-invariant subspace with basis B,...
Feb14-07 11:08 AM
matt grime
3 7,281
I have this matrix problem: Given R_1, R_2, R_3\in\mathbb{R}^{N\times N} are symmetric matrices with rank p<N....
May23-06 07:36 AM
1 7,279
I need to find the inverse of a 2x2 matrix of the form I'm halfway there, but the algebra gets really messy. ...
Sep24-08 09:51 PM
3 7,277
A function f between groups is said to be a homomorphism if it "preserves" the product in the sense that...
Aug2-10 05:58 AM
52 7,269
Claim: n! + 1 and (n+1)! + 1 are relatively prime. How can we prove this? Can we use mathematical induction? Base...
Jan14-10 01:09 AM
45 7,254
Quick question: is the nullspace the orthogonal complement of the column space or the the row space? Thanks, sorry...
Nov22-04 05:21 AM
2 7,244
Does anybody know of any jobs that deal explicitly with Matrices and/or Linear Algebra? I have to do a paper and I...
Oct19-07 12:43 PM
2 7,223
Just a conjecture... If any realizable real is built from the integers, then the single smallest positive real is:...
Jun21-04 01:22 AM
Jack Martinelli
16 7,221
write all possible equivalent conditions to "A is invertible," where A is an nxn matrix.
Nov7-07 07:55 PM
7 7,185
I'm working on some basic number theory. I came across an idea and I'm having trouble finding a general solution. A...
Jun28-07 11:08 AM
3 7,170
So I've shown that A and A^T have the same char. polynomials => same eigenvalues, using the fact that detA = detA^T. ...
Feb15-08 04:19 PM
2 7,159
The question: If G is the additive group Q/Z, what are the elements of the subgroup G(2)? Of G(P) for any positive...
Sep12-08 01:50 AM
1 7,153
I have a few questions to ask. They are simple, but the purpose is to make sure I'm staying on track. First, the...
Jan26-06 05:20 PM
44 7,144
0^0 = 1? ( 1 2 3 ... Last)
I've been told that any number raised to the zeroeth power is equal to 1. What about zero raised to the zeroeth...
May29-05 09:06 AM
matt grime
83 7,142
How would I calculate the determinant of a square matrix using LU Decomposition. Please be plain, I am not good with...
Aug20-09 10:11 PM
1 7,130
If you have two groups, G_1 and G_2 and A is a common subgroup, then you can form the free product of G_1 and G_2...
Oct25-06 10:30 PM
20 7,123
I know that the nth Fibonacci number is defined as: \frac{{1+\sqrt{5}}^{n}-{1-\sqrt{5}}^{n}}{{2}^{n}\sqrt{5}} ...
Jun23-11 07:35 PM
4 7,110

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