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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 35,756
X^3+PX+Q=0 X_0 = A + B (A+B)^3 + P(A+B) + Q = 0 A^3 + B^3 + (3AB+P)(A+B) + Q = 0 The next step is 3AB+P=0
Oct17-10 12:39 AM
3 3,023
I just started reading the first chapter of Georgi Shilov's "Linear Algebra" and I have a question about his notation...
Nov28-10 04:57 PM
3 2,842
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 1,367
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 1,295
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
3 776
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 2,020
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
3 925
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 1,901
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 1,274
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 5,744
0, 1, 1, 1, 2, 2, 4, 8, 12, 96... What number follows?
Sep5-10 03:11 AM
3 1,036
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
3 984
what will be the sum of this series? \Sigma nCr . 2r where r = 0 to n
Sep15-10 02:22 AM
3 1,169
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 1,058
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 4,262
I'm reading the first chapters of "A Guide to Distribution Theory and Fourier Transforms". On page 10, Exercises...
Sep19-10 01:21 PM
3 974
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 1,162
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 12,315
Here is my problem. Any ideas are appreciated. Let P be a projection matrix (symmetric, idempotent, positive...
Sep30-10 06:28 AM
3 6,888
not hw question and i say yes.
Oct28-10 03:52 PM
3 864
I read the following on the wikipedia page about simple rings ( I do...
Oct3-10 10:32 PM
3 1,126
Sounds great thank you
Oct3-10 04:28 PM
3 1,150
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 5,095
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
3 823
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 1,742
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 1,570
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 1,064
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
3 938
I expanded (x+y),(x+y) and got x^2+y^2 > 2xy then replaced 2xy with 2|x,y| but now I'm stuck. I need to get it to...
Oct15-10 10:14 AM
3 4,806
I think I understand most of this Wikipedia page on the interior product ("not to be confused with inner product"): ...
Oct17-10 02:01 PM
3 1,992
Since my late interests have been related to networks, I've started a pet project focusing on natural numbers network....
Oct21-10 03:27 AM
3 1,605
Hey there, physics forums! A question occurred to me the other day: Is it true that if f \in \mathbb{Z} is monic...
Oct21-10 05:26 PM
3 1,450
We have vectors x,y of size n and a matrix A of size nxn. Is it true that the matrix xyTA has at most one non zero...
Nov4-10 09:27 AM
3 1,509
Prove that the collection F(N) of all fi nite subsets of N (natural numbers) is countable.
Oct28-10 05:05 PM
3 2,147
Hi, I ran into conflicting definitions of integral domain. Herstein defines a ring where existence of unity for...
Nov7-10 04:10 PM
3 1,420
I was wondering, if we want to define a morphism from \mathbb{Z}2006 to, lets say \mathbb{Z}3008. Obviously, all...
Nov7-10 04:48 PM
3 1,189
Im struggling to find proof for this suspicion I have; Given is a function f(t) and a normalised function h(t), and...
Nov24-10 10:22 AM
3 1,738
Question: Show that if R is an integral domain then R^x=R^x(or that the units in R are precisely the units in R, but...
Nov19-10 08:49 AM
3 2,211
Some one please help me how to prove the following: \dot{A}:B + A:\dot{B}=A^{\nabla J}:B+A:B^{\nabla J} A and B...
Nov21-10 03:55 PM
3 3,549
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 2,196

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