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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
micromass
1 35,861
Hey! From MathWorld on solvable group: But why is that a special case? The way I understand it: the normal...
Sep18-13 07:48 AM
nonequilibrium
2 963
F(X1,...,Xn) is an invariant polynomial defined on the Lie algebra of a Lie group. The Xi here are left invariant...
Sep17-13 07:46 AM
lavinia
0 939
A is orthogonal if the A^{-1} = A^{T}. Thus, AA^{T} = I. However, is the statement A is orthogonal equivalent to...
Sep17-13 02:33 AM
UltrafastPED
1 1,123
Hello. I started Gallians Contemporary Abstract Algebra today. Is it wise to go through each of the given proofs for...
Sep17-13 01:56 AM
Bipolarity
1 980
Eigenstates of some observable O are represented by orthonormal vectors in complex Hilbert space. Is it true that...
Sep17-13 01:22 AM
James MC
6 1,089
Say I have a linear transformation T:V##\rightarrow##W. Can I necessarily say that T(V)##\subseteq##W? I feel like...
Sep16-13 01:43 PM
verty
6 1,186
I wanted to know if there is any way of classifying the set of all non-linear multivariable functions. I wish to...
Sep16-13 01:37 PM
fzero
1 876
Hello! Is there any nice proof that if belongs to the same vectorspace as A and B, then C is in the same...
Sep16-13 11:31 AM
fzero
1 1,030
I found that the cartan subalgebra of ##sp(4,\mathbb{R})## is the algebra with diagonal matrices in...
Sep15-13 12:12 AM
MathematicalPhysicist
4 978
The N real numbers x0, ..., xN-1 are transformed into the N real numbers X0, ..., XN-1 according to one of the formula...
Sep14-13 03:27 PM
mathman
1 760
Let G be a group and my book defines closure as: For all a,bε G the element a*b is a well defined element of G. Then G...
Sep14-13 02:57 PM
bonfire09
4 924
Consider a data matrix, X, with zero empirical mean. What is zero empirical mean? Could someone please give me...
Sep13-13 04:15 PM
mathman
1 938
if X= (3, 5, 7) & Y = (2, 4, 1) What is the 3x3 covariance matrix for X & Y?
Sep13-13 04:13 PM
mathman
7 1,080
I read that scalar matrices are the center of the ring of matrices. How would I prove this? Tips are appreciated. It...
Sep12-13 10:44 AM
Axiomer
1 1,359
http://en.wikipedia.org/wiki/Covariance I read from the above link that- The sample covariance of N observations...
Sep12-13 05:41 AM
DUET
6 997
Let ##T: V → V ## be a linear map on a finite-dimensional vector space ##V##. Let ##W## be a T-invariant subspace of...
Sep11-13 04:46 PM
Erland
1 818
Hello, I consider the groups of rotations R=SO(2) and the group T of translations on the 2D Cartesian plane. Let's...
Sep11-13 03:33 PM
mnb96
4 973
Is this true? I am studying direct sums and was wondering if the following statement holds? It seems to be true if one...
Sep10-13 11:58 PM
Office_Shredder
3 1,222
The identity map on the direct sum of V1 and V2 would be i1 composed with p1 + i2 composed with p2. Would such an...
Sep9-13 09:04 AM
economicsnerd
1 973
I'm curious about whether a statement I conjecture about direct sums is true. Suppose that ##V## is a...
Sep8-13 05:46 PM
economicsnerd
4 993
Hey, how would I graph the plane x + 2y + 3z = 0. We were taught to find the x,y and z intercepts and then connect...
Sep8-13 06:45 AM
baddin
2 881
Let xij be the ith independently drawn observation (i=1,...,N) on the jth random variable (j=1,...,K). These...
Sep7-13 12:39 PM
UltrafastPED
1 844
I've been thinking about a problem I made up. The solution may be trivial or very difficult as I have not given too...
Sep6-13 10:18 PM
brmath
3 946
Could someone please explain it to me what is the difference between Variance and Covariance?
Sep6-13 03:17 PM
mathman
3 867
Let V be a real vector space. Suppose to each pair of vectors u,v ε v there is assigned a real number, denoted by <u,...
Sep6-13 03:01 AM
DeIdeal
10 1,709
Let F be a field. R is an element of Mat(2,2) for a, b in F with matrix operations. a. Show that R is a...
Sep5-13 09:51 PM
brmath
5 903
Hi; How to raising a square matrix to the power of a complex number? for example: ^(1+i) or mathematics...
Sep4-13 11:02 PM
fzero
3 1,172
If two matrices similar to one another are diagonalizable, then certainly this is the case, since the algebraic...
Sep4-13 09:17 PM
brmath
2 1,016
Hi All, I have an equation like this: \sum_{i=0}^{n} x^{i}*y^{i} is there a way to re-express this equation...
Sep3-13 05:34 AM
Robert1986
3 1,089
Hi! I have a question concerning solving a system of linear equations. I know that the pseudoinverse matrix by...
Sep2-13 09:50 PM
brmath
2 957
Question regarding Kronecker Delta and index notation I am reading a book which covers the Kronecker delta and...
Sep2-13 08:51 PM
TheFerruccio
16 1,950
Hi, The following equations are from linear regression model notes but there is an aspect of the matrix algebra I...
Aug30-13 09:47 PM
chiro
1 742
Trying to make sense of the following relation: \sum log d_{j} = tr log(D) with D being a diagonalized matrix. ...
Aug30-13 05:57 PM
dm4b
3 785
The context in which this question arises (for me), is I was trying to take the curl of the magnetic field of a moving...
Aug30-13 05:43 AM
chiro
3 838
For example, if were given only a vector <5, 3, 1>, is this assumed to be respect with the standard basis of R^3? ...
Aug29-13 08:09 PM
Simon Bridge
10 1,058
Given A(m,n), eps = Machine Epsilon, fNorm = FrobeniusNorm(A), p >= 1 To filter noise near zero created by floating...
Aug29-13 11:44 AM
AlephZero
1 688
We know that the Newton binomial formula is valid for numbers in elementary algebra. Is there an equivalent formula...
Aug28-13 05:31 PM
francesco75
4 828
Hello folks, I'm not even sure if this is the place to put this but with some luck it might be. I just have a...
Aug25-13 07:28 PM
eigenperson
5 932
Hi, I have a matrix with N rows and K\cdot M \ll N columns. Is there a generic way to choose L rows s.t. the...
Aug25-13 02:34 PM
Stephen Tashi
3 873
Suppose that V and W are finite dimensional and that U is a subspace of V. If dimU≥dimV-dimW prove that there exists a...
Aug25-13 07:33 AM
HallsofIvy
6 1,069

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