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Linear & Abstract Algebra

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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 30,487
I am reading Dummit and Foote Ch 15, Commutative Rings and Algebraic Geometry. In Section 15.1 Noetherian Rings and...
Oct30-13 11:54 PM
Math Amateur
2 397
The two properties every linear transformation T: V -> W has to satisfy is T(u + v) = T(u) + T(v), for u,v in V (i)...
Feb17-14 04:01 PM
4 397
Exist so much theory for find the eigenvules of a matrix (invariants, characteristic polynomials, algebraic formula...
Feb24-14 01:57 PM
4 397
I am reading Dummit and Foote Ch 15, Commutative Rings and Algebraic Geometry. In Section 15.1 Noetherian Rings and...
Oct30-13 10:52 PM
Math Amateur
2 398
Hi everyone, I have a square matrix J \in \mathbb{C}^{2n \times 2n}...
Feb27-14 11:57 AM
0 398
I have begun to learn about maximal elements from a linear algebraic perspective (maximal linearly independent subsets...
Jun13-13 06:58 AM
1 399
Is any given finite semigroup isomorphic to some finite semigroup S that consists of some subsets of some finite group...
Jul24-13 07:13 PM
4 401
In a linear regression with 1 independent variable, if X is always the same (let's call I am unlucky), but Y present...
Jun26-13 03:57 PM
Number Nine
2 402
Hi everyone, I would like to ask you something about vector spaces. I have the following term: S=dim(R(...
Aug2-13 10:19 AM
0 403
Here it is for those interested.
May28-13 08:47 AM
0 404
Let's say I have a matrix M such that for vectors R and r in xy-coordinate system: R=Mr Suppose we diagonalized it...
Jul24-13 12:19 PM
2 404
Hi, Could anyone give me a proof for the following theorem? Theorem : Ax=0 has a non-trivial solution iff det(A)=0...
Mar27-14 06:47 AM
2 404
In "Quantum Computation and Quantum Information" by Nielsen & Chuang, on pp. 88-89, applying basic statistical...
Mar19-14 04:06 AM
2 406
Hi all, I'm testing out a matrix solving program and while it checks out for 2x2/3x3/4x4 I would like to try it out...
Jun12-13 06:12 AM
Kosh Naranek
1 408
If I have two square nonnegative primitive matrices where the Perron-Frobenius Theorem applies how would I calculate...
Jul4-13 09:01 PM
Simon Bridge
2 408 The proof is showing that particular matrix ring is not left...
Oct27-13 11:10 AM
0 408
Suppose we have $$=if^c_{ab}Q^c$$ where Q's are generators of a Lie algebra associated a SU(N) group. So Q's are...
Jul24-13 02:01 PM
0 411
Suppose I have some functions ## \{ y,y_{1},y_{2},...y_{n} \} \subset C^{∞} ## and suppose I know that the Wronskian...
Jul30-13 12:42 PM
1 412
I am reading Dummit and Foote (D&F) Section 15.1 on Affine Algebraic Sets. On page 662 (see attached) D&F define a...
Nov2-13 09:37 AM
1 412
Hi guys, So as title states, how would one sketch Re(iz) = 3? And an explanation would be splendid. This is what I...
Feb6-14 09:35 PM
5 412
Friedberg proves the following theorem: Let V and W be vector spaces over a common field F, and suppose that V is...
Jun10-13 12:25 PM
1 413
Hello! I ve come across with something called ' relative element of a vector' Could you provide me a definition and...
Jul25-13 04:27 PM
Stephen Tashi
1 413
Hi all, Im trying to think of a way of generating non-intersecting randomly oriented cylinders within a unit cell...
Feb12-14 07:06 AM
9 413
I was developing a pythagorean theorem proof based on the cross product of two vectors..Below is my final...
Feb1-14 09:03 PM
3 414
When I start to read the the article called "symmetric bi-linear forms", I face the following sentence. But I don't...
Aug4-13 11:49 PM
3 415
I'd like to figure out why f(x) = x^n - r e^{i \theta} = \prod_{j = 0}^{n - 1} ( x - r^{1/n} e^{i \theta / n} e^{2...
Feb9-14 03:33 PM
2 416
Let's say we randomly select integers to construct a potentially infinite number, for example 3588945.... There is a...
Apr4-14 12:59 PM
2 416
I have some question guys i have four points in the x,y plane in cartesian coordinates. A (Ax,Ay) B(Bx,By) ...
Jun17-13 05:18 AM
5 417
delete please
Feb6-14 02:24 PM
1 417
Using the given information, is it possible to solve the new travel direction of the smiley face? To clarify, I am...
May29-13 06:48 PM
Simon Bridge
6 418
I have some reason to believe that \det(\textrm{id} + AB) = \det(\textrm{id} + BA) is true even when AB and...
Jun20-13 10:47 PM
2 418
For another thread , I want to give simple motivations for the...
Jun23-13 01:19 AM
Stephen Tashi
3 418
I was having a quick look at Isaacs : Algebra - A Graduate Course and was interested in his approach to Noetherian...
Oct31-13 01:02 AM
3 418
Wasn't sure whether to post this in the computing section or not but here goes anyway, I have n number of 2d...
Feb5-14 07:14 AM
2 418
For a linear transformation to be invertible, is it a requirement that the domain and codomain be the same vector...
Jun11-13 08:26 AM
3 419
Hi, I'm getting a bit confused about the adjoint representation. I learnt about Lie algrebras using the book by...
Aug2-13 03:24 PM
0 419
0\rightarrow A\rightarrow B\rightarrow C\rightarrow 0 is a short exact sequence if the image of any morphism is the...
Dec12-13 01:07 PM
2 419
Hi all! I have no application in mind for the following question but it find it curious to think about: Say that...
May31-13 06:43 PM
1 420
Using this coordinate system and writing the relationships: \vec{\rho}\;'=R^{-1}(\phi)\vec{\rho} \begin{bmatrix}...
Jan27-14 09:18 AM
2 421
Not sure if this is the right subforum. This is technically a signal processing question, but it edges on proving...
Apr7-14 11:24 AM
12 421

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