
Please post any and all homework or other textbookstyle problems in one of the Homework & Coursework Questions...

Feb2313 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...

Sep1813 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...

Sep1713 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...

Sep1713 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...

Sep1713 01:56 AM
Bipolarity

1 
980 
Eigenstates of some observable O are represented by orthonormal vectors in complex Hilbert space.
Is it true that...

Sep1713 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...

Sep1613 01:43 PM
verty

6 
1,186 
I wanted to know if there is any way of classifying the set of all nonlinear multivariable functions. I wish to...

Sep1613 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...

Sep1613 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...

Sep1513 12:12 AM
MathematicalPhysicist

4 
978 
The N real numbers x0, ..., xN1 are transformed into the N real numbers X0, ..., XN1 according to one of the formula...

Sep1413 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...

Sep1413 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...

Sep1313 04:15 PM
mathman

1 
938 
if X= (3, 5, 7) & Y = (2, 4, 1)
What is the 3x3 covariance matrix for X & Y?

Sep1313 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...

Sep1213 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...

Sep1213 05:41 AM
DUET

6 
997 
Let ##T: V → V ## be a linear map on a finitedimensional vector space ##V##.
Let ##W## be a Tinvariant subspace of...

Sep1113 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...

Sep1113 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...

Sep1013 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...

Sep913 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...

Sep813 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...

Sep813 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...

Sep713 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...

Sep613 10:18 PM
brmath

3 
946 
Could someone please explain it to me what is the difference between Variance and Covariance?

Sep613 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,...

Sep613 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...

Sep513 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...

Sep413 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...

Sep413 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 reexpress this equation...

Sep313 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...

Sep213 09:50 PM
brmath

2 
957 
Question regarding Kronecker Delta and index notation
I am reading a book which covers the Kronecker delta and...

Sep213 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...

Aug3013 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.
...

Aug3013 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...

Aug3013 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?
...

Aug2913 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...

Aug2913 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...

Aug2813 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...

Aug2513 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...

Aug2513 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≥dimVdimW prove that there exists a...

Aug2513 07:33 AM
HallsofIvy

6 
1,069 