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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 35,885
If we consider a number 9999999. infinite times then no other number that can be represented bigger than that...
Nov24-12 08:04 PM
9 2,470
Hi guys, Let's say I have a 6x6 matrix A whose Jordan form J has 3 Jordan blocks. It means that this matrix (matrix...
Dec3-12 10:24 PM
18 3,181
Hi, I just need help understanding one line of the...
Nov26-12 01:20 PM
0 722
How are orbits and cosets related? Are all orbits cosets? Are all cosets orbits? Also, what exactly are G-sets and...
Nov30-12 10:09 AM
1 1,152
Hey, here's a simple question. I have been reading some materials and, for the n-th time in my life, there was a...
Nov20-12 11:19 AM
15 1,625
let P(n) = n^4 + an^3 + bn^2 + cn M(a,b,c) returns largest m that divides P(n) for all n then let function S(N)...
Nov21-12 07:32 AM
2 1,826
This is not a homework question ..... If two vector spaces, say V and W, have equal cardinality |V|=|W| .... do...
Nov21-12 07:41 PM
2 1,231
It is defined that for any matrix A, A^{0} is defined as being equal to the identity matrix, I My question: Does...
Nov21-12 05:32 PM
18 2,056
Matrix A= 2 1 2 1 2 -2 2 -2 -1 It's known that it has eigenvalues d1=-3, d2=d3=3 Because it has 3...
Nov22-12 02:16 PM
6 2,763
I have Theorem 1 from a research paper. Theorem 1. Suppose that G is a finite non-abelian simple group. Then there...
Nov20-12 01:04 PM
0 851
Why is that Nullspace of A is subset of nullspace of A^T*A let's say that A is m*n matrix
Nov20-12 09:54 PM
2 939
if A is a tridiagonal Matrix , what does this mean ? what does tridiagonal mean in matrix ? what is the property...
Nov22-12 11:40 AM
2 1,009
How do you find matrices a,b,c satisfying a=b*c*b^-1 b=c*a*c^-1 c=a*b*a^-1 ?
Nov22-12 03:33 AM
2 879
If I have (for simplicity) a vector ( A, B) where A and B are matrices how does the transpose of this look, is it (...
Nov21-12 06:14 PM
6 1,247
I have a vector (1,i) and need to normalize it. I am being told that the answer is 1/(sqrt(2)) (1,i) but it seems...
Nov24-12 05:21 AM
3 972
Ok there is no way I am writing out all the work of this question using a keyboard, and my scanner chose today not to...
Nov25-12 06:33 PM
4 1,553
I have solved the roots of a quadratic equation and want to "test" them by putting them back in for x. I am having a...
Nov23-12 08:30 PM
5 1,267
Hi. In Apostol's book "Introduction to analytic number theory", Teorem 3.2(b), Apostol proves (1) \zeta (s) =...
Nov24-12 08:11 PM
1 1,161
Hey! Let M and N be two natural numbers and N>M. I want to build a set A with N vectors of size M such that each...
Nov27-12 08:37 AM
2 1,375
Hi, if we suppose x and y are two elements of some vector space V (say ℝn), and if we consider a linear function...
Nov27-12 12:01 PM
2 1,024
Is there a nice closed-form for this?
Nov26-12 06:05 PM
3 1,903
wrtie down the possible isomorphism types of abelian groups of orders 74 and 800 then for 74=2*37 then Z(74) is...
Nov25-12 06:09 PM
2 1,606
Linear transformation f:C^∞(R) -> C^∞(R) f(x(t)) = x'(t) a) I have to set up the eigenvalue-problem and...
Nov27-12 08:16 PM
2 1,011
Hello, I want to find a family of functions \phi:\mathbb{R} \rightarrow \mathbb{C} that have the property:...
Nov28-12 03:30 PM
14 1,800
I am having trouble understanding a section in these notes: . It is on page 3. Section 3 -- Discretization of the...
Nov25-12 07:07 PM
0 999
I thought it would be obvious, but I can't find a series representation of the Laplace transform. I'm looking for...
Nov29-12 08:48 AM
2 1,034
Sorry about the long title. I recently had a few homework problems which were similar to the title of the post. I...
Nov27-12 02:46 PM
1 702
Ok I understand the concept of infinite countability and that say the set of all rational #s is infinitely countable,...
Nov27-12 05:43 PM
1 1,664
I have two 3d applications and when an object(a cube for example) is transferred between them, the rotation values of...
Nov28-12 08:06 AM
3 813
It's very difficult for me to find any simple literature to explain this idea. J\inMn(ℂ) is a coninvolutory (or a...
Nov29-12 01:42 PM
4 927
Hello, let's suppose I have two functions f,g\in L^2(\mathbb{R}) and I consider the inner product \left\langle f,g...
Nov29-12 06:54 PM
Stephen Tashi
7 1,421
Given two systems, Ax=b and Cy=d, for nxn matrices A and C, and n-dimensional vectors b and d, each of which has at...
Dec1-12 12:21 PM
1 900
The following problem was given on a test of mine and I got it completely wrong. If anyone can help me with solving...
Nov29-12 06:09 PM
1 788
After solving some problems about matrix invertibility and learning some theorems (and proving them), I have developed...
Dec1-12 01:22 PM
2 826
Hi guys I wonder if you know any linear algebra formalism or something to solve the following question...
Dec3-12 10:37 AM
3 1,012
I now know that inverses are only defined for square matrices. My question is: is this because inverses for non-square...
Dec2-12 06:57 AM
8 1,115
let A_i be an odd integer, s_i be the square of a_i and t_i be the triangular number, (s_i -1)/8. Same for a_j , s_j,...
Dec1-12 10:25 PM
2 1,402
At first I thought that there is no square matrix whose square is the 0 matrix. But I found a counterexample to this....
Dec2-12 12:37 PM
5 1,099
the question is , if f(n)= 1+10+10^2 +... + 10^n , where n is integer. find the least n s.t. f(n) is divisible by 17...
Dec5-12 09:33 AM
3 1,332
Hi, If A is some nonsquare matrix that is possible rank-deficient, then am I right to understand that (A^T)(A) is a...
Dec5-12 09:16 AM
1 1,844

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