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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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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 30,402
I have to prove that x*0= 0 where x is any integer. I can do this pretty easily using the proposition that m(-1)=-m...
Jul19-09 11:24 PM
epkid08
3 2,930
I don't know if this has been posted already, but anwho... If you pick any positive integer greater than 9 and...
Jul23-09 05:38 PM
JazzFusion
8 14,271
This is a mental arithmatic question really, but what is the fastest way you have found to multiply two numbers in...
Jul9-09 12:15 PM
Count Iblis
7 3,384
In chapter five of Douglas Hofstadter's book Goedel, Escher, Bach, the author poses a question about...
Jul8-09 07:11 AM
torteloni
3 4,039
Is anything more known about Legendre's conjecture that there is a prime between n^2 and (n+1)^2 for positive integers...
Jul21-09 01:50 PM
CRGreathouse
3 3,452
What's the difference between a point and a vector (both of which are situated in 3-Dimentions)? I mean, they are...
Jul9-09 08:07 PM
romistrub
35 39,939
Other than the Riemann Zeta function, what equation has a non-trivial infinity of zeroes with real part one-half?
Jul23-09 04:55 PM
Petek
15 2,732
What is the basis for the vector space of all continuous functions?
Jul18-09 10:08 PM
John Creighto
15 1,793
It might be a silly question but I was just wondering if this was unprovable or false... Thanks guys
Jul10-09 04:08 PM
camilus
9 2,488
My work is on implicit FDTD method which allows time step (delta_t) above CFL limit. Implicit methods require one to...
Jul23-09 12:43 PM
confi999
0 812
what exactly is the number zero? I mean, the number 0 seems to negate the absence of meaning in the digital world...
Jul11-09 04:02 PM
camilus
13 12,209
let be X,Y and Z operators of some algebra so = \epsilon _ijkX_k where i,j and k range over X, Y and Z then i...
Jul8-09 01:27 PM
HallsofIvy
1 899
Hi Everyone, I am facing a basic level problem about direction cosine matrix as I am not an expert in mathmatics....
Jul8-09 07:50 AM
stiltz
0 4,100
Please anyone solve this question or can even email me on my ID abu_95bakar@yahoo.com... For the following question...
Jul8-09 09:22 AM
HallsofIvy
1 757
Suppose T ∈ L(V) and U is a subspace of V. Prove that U is invariant under T if and only if U⊥ is invariant under T∗....
Jul13-09 01:45 PM
evilpostingmong
3 1,036
Say we have a transformation T\inL(V). Now suppose a subspace of V (U) is in the rangespace of T. Now suppose PUv=u...
Jul9-09 09:47 AM
evilpostingmong
4 855
I have graphed something in mathematica and when plotting I accidentally told it to plot the x and y axes backwards-...
Jul8-09 10:12 PM
Phrak
1 947
In polynomial interpolation: I see some connection between: The Vandermonde matrix, the monomial basis and the...
Jul9-09 10:56 AM
trambolin
1 2,559
Hello, I don't quite understand this stuff but have managed to get to the point where the chart appears to be a...
Jul11-09 08:05 PM
docspidey
0 950
Hi. if anybody can help me Let S be the matrix a b c d with a constrain a =...
Jul14-09 12:23 PM
jj48
8 1,599
In Linear Algebra and its Applications, David Griffel writes, "The components of covectors are often denoted by...
Jul16-09 10:42 AM
Rasalhague
2 1,176
given the Selberg trace formula \sum_{n=0}^{\infty} h(r_n) = \frac{\mu(F)}{4 \pi } \int_{-\infty}^{\infty} r \,...
Jul14-09 07:35 AM
zetafunction
0 1,232
Hi All, this is not homework, just some basic revision for my own personal understanding, it's a long time since I...
Jul17-09 04:30 PM
Auto Engineer
2 754
How would you write the following using index-notation? s \cdot F \cdot u Given that s = (s^0, \vec{s}) and u...
Jul14-09 09:32 AM
smithg86
0 909
Given a 4x4 non-Hermitian matrix, is there any method I can use to prove the eigenvalues are real, aside from actually...
Jul15-09 08:51 AM
andrewm
2 1,350
I need to find a way to sum/ a closed form representation for: \sum^{N}_{n=1}\frac{\Gamma(n-s)}{\Gamma(n+s)} ...
Jul15-09 01:13 AM
CRGreathouse
1 1,842
Hi, in the text I am reading I found the following implicit definition of an adjoint transformation: \overline{f}(...
Jul16-09 02:04 AM
mnb96
4 2,868
I spend some time studying special functions recently. I found two definitions of gamma function, one in form of...
Jul15-09 11:37 AM
LHS1
2 1,043
Sorry, I have mistakenly posted it in the General Math forum. This was my fault. As I do not know how to correct...
Jul15-09 03:04 PM
Luca
0 1,549
Hello PF members This is my first post. It is rather complicated to understand but I request you to bear with me. ...
Jul17-09 04:48 PM
Hurkyl
1 691
Hi everyone, could someone please advise; The equation; PA - P atm A = K, change in X If I wish to factor...
Jul18-09 11:31 AM
Auto Engineer
4 1,416
Hello everyone, I have a query regarding the Gram-Schmidt factorization: Say I have 3 independent vectors, u, v,...
Jul19-09 04:52 PM
HallsofIvy
2 1,508
What is the geometric interpretation of unimodular matrices?
Jul20-09 03:42 PM
Dragonfall
4 1,129
is the following sequence finite \sum_{n=1}^{\infty} \frac{log^{u-1} (n)}{n} - u^{-1}log^{u}(n) if u=1 then we...
Jul22-09 06:57 AM
zetafunction
2 1,241
I had this question on a test and I was wondering why it is false: If the row space equals teh column space then...
Jul20-09 06:48 PM
slider142
3 1,163
A matrix is diagonalizable when algebraic and geometric multiplicities are equal. I know this is true, and my...
Jul21-09 05:52 AM
HallsofIvy
2 1,328
A matrix is diagonalizable when algebraic and geometric multiplicities are equal. My professor proved this in class...
Jul23-09 03:59 AM
trambolin
2 3,422
I'm a bit confused as to how to calculate the 2nd chebyshev function. I know \psi (x) = \sum_{p^k \le x} \ln p ...
Jul21-09 07:23 PM
g_edgar
1 1,261
(aT)∗ = \bar{a}T∗ for all a ∈ C and T ∈ L(V,W); This doesn't make much sense to me. Isn't a supposed to be=x+iy and...
Jul22-09 02:31 PM
HallsofIvy
3 969
I have this problem where I'm having trouble solving so any help would be appreciated. Here's the problem: You...
Jul22-09 05:00 PM
CRGreathouse
2 1,992

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