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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'm Yr 13 and just wanted to do some further reading/exploring. So i understand that the zeta function is...
Aug19-12 01:34 AM
19 7,694
Do all linear transformations are matrix transformation? In a book by David C Lay, he wrote on page 77 that not all...
Aug2-12 04:21 PM
5 6,165
Hi, I need help with matrix derivation. I have 2 matrices of dimension 2x1, A and B. A = ^{T} B = ^{T} I would...
Aug9-12 12:53 PM
5 2,891
X^4-(X^3)y+(X^2)(y^2)-x(y^3)+y^4= (x+y)^4-5xy(x+y)^2+5(xy)^2 ...
Aug13-12 07:51 PM
5 3,428
Hi I am trying to learn about quotient groups to fill the gaps on things I didn't quite understand from undergrad....
Aug14-12 10:16 PM
7 1,391
Def: A low discrepancy sequence is a uniformly distributed sequence with minimal discrepancy, O(logN/N). Question:...
Aug2-12 03:26 PM
3 1,294
Okay so I'm a first year engineering student and I'm taking linear algebra. I understand how to take determinants...
Aug8-12 11:03 PM
11 1,705
I originally asked this in the Calculus & Analysis forum. But perhaps this is better suited as a question in Abstract...
Aug5-12 12:12 AM
6 1,765
For an arbitrary distance the equation is: \sqrt{\Sigma_{i}^{n}x_{i}^{2}} I would like to know what are the...
Aug1-12 04:12 PM
5 1,017
I am having trouble understanding the permutations of a finite set in general. I want to know what it may be used for,...
Aug3-12 01:59 PM
3 1,042
First,could you please clear this doubt- A polynomial with rational coefficients does not form a vector space over...
Aug2-12 09:47 PM
4 1,240
Students familiar with Euclidean space find the introduction of general vectors spaces pretty boring and abstract...
Aug9-12 12:10 PM
2 1,207
Hello All: Suppose I have a completely known linear system: A*x=b. I know the matrix A, and an x and the associated...
Aug1-12 03:35 PM
4 649
Attached is a graph of the number of goldbach partitions versus Hardy Littlewoods asymptote for even numbers of the...
Aug1-12 09:44 PM
Paul Mackenzie
0 1,192
Consider the following sequence, where the elements are rational numbers mulriplied by \pi: (\alpha_{i}) = \hspace{2...
Aug3-12 09:17 AM
2 1,306
Let us take the most mainstream irrational out there, (Pi). Now write (Pi) as: 3. 14159265... Let us number...
Aug5-12 07:34 AM
3 1,676
Hello, this is rather vague but I had a lecture around a year ago about prime numbers and how a mathematician (Hardy...
Aug7-12 11:44 PM
4 2,307
This is very weird, but I found an inconsistency in the application of Cramer's Rule for a 3x3 simple linear matrix. ...
Aug10-12 10:03 AM
3 965
Hi, I have to take a placement exam in linear algebra this fall so I have been studying some past exams. This is a...
Aug8-12 12:06 PM
4 948
I have been investigating goldbach partitions for some time. One interesting observation I have been able to...
Aug9-12 05:27 AM
Paul Mackenzie
2 1,456
Is there a way to define in how many ways can I form a number by it's portions? e.g: the number 5 has 6 ways:...
Aug8-12 05:17 PM
4 1,366
There's a geometric interpretation of the determinant of an operator in a real vector space that I've always found...
Aug9-12 03:09 PM
6 1,366
Hi, I have this problem that is solved, but I don't understand the theory behind it. It says: Which of the...
Aug8-12 07:32 PM
5 998
What is eigen value, eigen vector etc and what is their physical significance? -Devanand T
Aug11-12 05:57 AM
8 1,861
I was thinking about identities, and seem to have arrived at a contradiction. I'm sure I'm missing something. A(n)...
Aug11-12 12:50 PM
8 1,307
I have been having trouble of late with partial fraction decomposition. Not so much the maths, but the intuition...
Aug11-12 01:37 PM
2 873
Suppose we have a finite dimensional inner product space V over the field F. We can define a map from V to F...
Aug11-12 08:13 PM
3 1,025
Let a, b and c be positive integers such that a^(b+c) = b^c x c Prove that b is a divisor of c, and that c is of the...
Aug12-12 05:10 AM
2 1,344
The isomorphism of ℝ5 and P4 is obvious for the "standard" inner product space. The following question arise from...
Aug18-12 09:58 PM
3 963
I was perusing the internet and I came across a formula for the area of triangle in a coordinate plane. With...
Aug13-12 11:36 AM
1 905
if a, b, c (integers) are coprimes then (an + bn + cn ) / abc can't be a number that is not a fraction (integer)....
Aug15-12 08:55 PM
2 1,574
I have a small idea on what irreducible and primitive polynomials are in Abstract algebra. But what is minimal...
Aug14-12 09:22 AM
2 820
Can any one clarify the concepts of zero vector and zero scalar? -Devanand T
Aug18-12 10:13 AM
3 2,013
Hello fellas. I have this formula that encodes data: OUTPUT = (Data * 7) + (Data * 2) + 8 So in this case, if...
Aug14-12 06:11 AM
3 733
If H is a Hermitian operator, then its eigenvalues are real. Is the converse true?
Aug17-12 03:23 AM
2 1,086
Can anyone tell me how can i find a solution to a transcendental equation? Any link, where i will get methods to...
Aug15-12 07:13 AM
2 1,015
Hello, I have a doubt on the definition of Lie groups that I would like to clarify. Let's have the set of...
Aug15-12 05:09 AM
4 872
Let p be a prime. Let H_{i}, i=1,...,n be normal subgroups of a finite group G. I want to prove the following: If...
Aug16-12 10:10 PM
3 1,024
My question is about the shaded area in the attachment? How did the author get that all the elements of order p or 4...
Aug18-12 12:04 PM
2 915
If I know that \sum_{k=1}^n a_{ik} = 1 and \sum_{j=1}^n b_{kj} = 1, why is the following permitted? \sum_{j=1}^n...
Aug18-12 11:04 AM
2 799

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