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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 36,226
I currently self study from the book "A Course in Modern Mathematical Physics" by Peter Szekeres, and I'm currently...
Aug5-10 02:28 PM
3 1,631
Dear Friends, I have a question and would be pleased if you help me by suggesting a paper or book to study. Let...
Aug18-10 11:52 PM
3 4,475
I'm trying to compute the eigenvalues for a 32x32 symbolic matrix (with one variable) in Mathematica. I get the...
Aug1-10 08:23 PM
3 3,886
I need help. So the obvious answer is no, because it's not integrally closed (incidentally it's integral closure...
Jul16-10 12:19 PM
3 1,455
given any two numbers a,b and an upper and lower bound for the sum of reciprocals of a certain class of integers...
Jul21-10 11:21 PM
3 3,663
Anyone know how to solve a quintic or quartic? (thanks) (try to list your information, its helpfull!)
Jul17-10 02:49 AM
3 1,481
I googled for a proof,but didn't find one. Could anyone give me a link to a proof?
Jul23-10 04:00 AM
3 6,967
Would you please help me? Thanks in advance. Prove that if a belongs to R, then (a^2)^1/2 = |a|? by using...
Aug1-10 09:15 PM
3 1,523
Hey all, I'm trying to find an orthogonal complement (under the standard inner product) to a space, and I think...
Aug2-10 11:44 AM
3 3,144
What is the effect on a vector when it is multiplied by a matrix? Let any matrix 2 3 3 5 What will be the...
Aug4-10 05:28 PM
3 1,366
Is it correct that the Gaussian elimination procedure is used in computer software to solve systems of linear...
Aug6-10 03:36 PM
3 1,331
I'd like to do one of two things: 1: Find an example of a non-diagonal matrix whose matrix exponential (defined in...
Aug10-10 02:52 PM
3 2,566
Suppose \mathfrak{g} and \mathfrak{h} are some Lie algebras, and G=\exp(\mathfrak{g}) and H=\exp(\mathfrak{h}) are Lie...
Aug10-10 08:45 AM
3 910
The number of partitions of an even number 2N into N parts appears to be equal to the number of partitions of N. ...
Aug17-10 01:34 PM
3 3,316
I am looking for a rather simple proof that if the matrix A has eigenvalues>0, then (x^t)Ax>0 for any vector x not 0....
Aug23-10 08:00 AM
3 1,380
Thank you for reading. If I have an object (is it correct to call it a tensor?) whose components are defined by: ...
Aug26-10 12:55 AM
3 1,300
I'm currently learning Lie groups/algebras and I am trying to find the infinitesimal generators of the special...
Aug22-10 11:05 PM
3 901
There is a problem in a book I'm not quite understanding. Let M be an R-module and let I=Ann(M). Show that M can be...
Aug26-10 03:58 AM
3 788
normal extension - an algebraic field extension L/K is said to be normal if L is the splitting field of a family of...
Aug30-10 05:57 AM
3 2,043
Help for prove this please Let T\in{L(V,W)} The equation Tx=y have one solution iff y\in{R(T)}
Aug28-10 12:41 PM
3 934
Yet another silly question from me :/. From an instructor's notes: "Let V = R^n be the vector space of column n-tuples...
Sep1-10 02:39 PM
3 1,925
Definition: A semigroup is a pair (R,op) where R is a set an op is a binary operation that is closed and associative. ...
Sep8-10 06:27 AM
3 1,284
Consider a binary operation on a set G. A an element e of G is said to be a left identity if ex=x for all x. If x is...
Sep4-10 08:53 PM
3 5,806
0, 1, 1, 1, 2, 2, 4, 8, 12, 96... What number follows?
Sep5-10 03:11 AM
3 1,044
Are there cases where there's more than one binary operation to choose from by which to define a Lie algebra for a...
Sep10-10 10:47 PM
3 999
what will be the sum of this series? \Sigma nCr . 2r where r = 0 to n
Sep15-10 02:22 AM
3 1,176
Appoint all the pairs (k, l) (both k and l in R^+) such that: \sqrt{k}+\sqrt{l}=\sqrt{4+\sqrt{7}} I'm really stuck...
Sep12-10 09:44 PM
3 1,062
I was wondering what would be the largest possible value for a determinant, for a 3 by 3 matrix whose entries can only...
Oct11-10 06:42 PM
3 4,299
I'm reading the first chapters of "A Guide to Distribution Theory and Fourier Transforms". On page 10, Exercises...
Sep19-10 01:21 PM
3 983
what is another way to form (a+b)^c to another simple expression? like for example a^c+b^c doesnt work because its...
Sep20-10 10:12 PM
3 1,164
When I realize that I am going to have a singular matrix (after exhausting row swap options and maybe even some...
Sep22-10 09:50 PM
3 12,518
Here is my problem. Any ideas are appreciated. Let P be a projection matrix (symmetric, idempotent, positive...
Sep30-10 06:28 AM
3 6,966
I read the following on the wikipedia page about simple rings ( I do...
Oct3-10 10:32 PM
3 1,144
Sounds great thank you
Oct3-10 04:28 PM
3 1,156
Hello everyone. I was going through my Linear Algebra Done Right textbook that threw me off. I hope this forum is...
Oct4-10 11:17 PM
3 5,147
Is it true that if a finite group G contains a subgroup of index 2, then there is an element of G with order 2?
Oct8-10 10:08 AM
3 834
I saw the following problem on my abstract algebra book (dummit && foote) , I tried to solve it but I couldn't : Let...
Oct11-10 04:03 AM
3 1,768
Let V be a finite-dimensional vector space over the field F and let T be a linear operator on V. Let c be a scalar and...
Oct12-10 12:49 PM
3 1,586
Do all linearly dependent sets have elements that are linear combinations of each other? Or does this apply only to...
Oct12-10 10:21 AM
3 1,077
Can i use the invertability of a matrix as an alternative way of determining the linear independence of a set? Thank...
Oct12-10 10:54 AM
3 952

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