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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
1 30,435
How do you proove what the idempotents of the ring Z/100Z are? I know by trial and error that they are the elements...
Apr14-08 11:20 AM
1 1,083
In the following 0/1 matrix I'm trying to identify every largest submatrices formed by 1's as shown in the picture. ...
Apr6-14 12:20 PM
1 205
3.5036799918564934004113 I need help identifying this real number. The closest I have gotten is e+pi/4. But I...
Dec9-12 11:53 PM
9 1,819
Hi, everyone: I have been playing around with tensor products of vector spaces recently. This question came up:...
Dec21-07 10:31 AM
4 1,625
The question is to prove for finite dimensional T: V to W, T is injective iff there exists an S: W to V such that ST...
Mar4-09 04:16 AM
12 3,532
it is true in general that the sum (density of states for a physicst) \sum_{n=0}^{\infty} \delta (x- \gamma _{n}) ...
Dec14-08 06:40 AM
1 1,731
If TP conjecture is false and there're only a finite number of primes then..could we write the sum of the reciprocal...
Sep16-06 01:21 PM
0 2,103
I want to show that if 1 were a congruent number then there would be an integer solution to the equation x^4-y^4=u^2...
Mar20-11 09:03 AM
3 1,211
Hi, can anyone explain to me if a 3 x 4 matrix can have independent columns? How about independent rows? Thanks!
Apr13-10 05:52 PM
3 695
I think this is true but not sure how to prove it. Suppose that A and B are both totally unimodular matrices then is...
Nov10-11 11:02 PM
0 814
if A is a tridiagonal Matrix , what does this mean ? what does tridiagonal mean in matrix ? what is the property...
Nov22-12 11:40 AM
2 848
Theorem: If A is a nilpotent square matrix (that is for some natural number k>0, A^k =0) then (I + A) is an invertible...
Oct25-07 03:45 PM
11 4,517
Suppose it is known that A is singular. Then the system Ax=0 has infinitely many solutions by the Invertible Matrix...
Dec15-12 01:09 PM
4 1,043
Hi I am arguing with a friend about the following: He claims that if a mxn matrix A, m>=n has a reduced...
Sep23-10 03:08 PM
4 1,524
This is certainly an elementary question, so I would be all the more grateful for the answer. Given: A and B are two...
Feb24-14 03:39 AM
2 420
well this is the question... if a,m and n are positive integers with m<n, then (a^(2^m)+1) is a divisor of...
Oct28-09 12:22 AM
1 1,112
I'm not sure I've convinced myself here. Take the L be the set of all linear transformations from V -> V, where V...
Oct14-08 05:03 PM
Pere Callahan
16 1,260
If AB is invertible, then A and B are invertible for square matrices A and B. I am curious about the proof of the...
Sep27-13 02:57 PM
14 5,250
I'm looking for help to this problem. Here is my attempt: I being the identity matrix and B^(-1) being B to the...
Oct20-11 11:07 PM
2 1,646
I am curious: if f and g are (complex) orthogonal functions, are f* and g also orthogonal? (* denotes complex...
Sep29-13 10:27 AM
2 551
hi if F is inner automorphism , what does this mean ? I think that if F : G to G then we can write F(x) as ...
Dec16-12 04:55 PM
Maths Lover
2 756
this is how i set up the problem, am i thinking correctly? for all h belong H b,a belong to G where Ha and Hb are...
Nov1-07 06:48 AM
matt grime
11 2,821
--> if n = x(mod 10x+1) n,x>0 (where = is symbol used in "congruence" not equality) then, is there a way...
Apr5-12 04:58 AM
1 1,357
If n*n matrix, can row space ever be equal to null space? P.S.: this is NOT a homework question. It's a general...
Apr7-10 02:27 PM
5 2,591
If like DTn,d = pochhammer(n,d)/d! For the triangle number in any dimension is true Then whats say a simple root...
Oct21-12 12:06 AM
0 1,039
Hi. I need to: prove the group (Zp*,x) has exactly one element of order 2. Here, p is prime and (Zp*,x) is the set {1,...
Nov26-11 03:26 PM
3 1,784
I have just had linear algebra exam, and one of the questions was to prove or disprove (give a counterexample) that if...
Oct30-06 10:33 AM
2 1,922
If the z-transform of x is X(z), then what is the z-transform of x in terms of X(z) ?
Dec12-08 12:31 PM
4 4,350
If two matrices are similar, it can be proved that their determinants are equal. What about the converse? I don't...
Jul24-13 07:56 PM
5 1,109
The book I am going through says this : The below proposition is false for real inner product spaces. As an...
Dec28-12 06:46 PM
3 886
I defined the angle \theta between x \in \mathbb{R}^k and y \in \mathbb{R}^k in the way that: \theta = \cos...
Aug3-11 10:19 PM
1 1,116
Ok so I have an assignment for my Calculas/Geometry class and I seem to have not paid the greatest attention in class...
Jan3-08 09:37 AM
2 1,375
Is it true that if \sigma \in S_n is a cycle of length k \leq n, then \sigma^k = \varepsilon, where \varepsilon is the...
May28-09 01:04 AM
matt grime
5 1,310
If x,y are (2,2) complex matrices such that log(xy)=log(x)+log(y) then x,y commute
Dec4-07 07:44 PM
Count Iblis
0 2,434
If we knew the prime number counting function \pi(x) then how could we recover the n-th prime?..of course an easy...
May6-06 08:07 AM
7 1,761
Im new to theese forums and kindof new to number theory because im only a junior in highschool. so is there any...
Dec5-04 02:25 AM
3 1,599
Let R be a ring of characteristic m > 0, and let n be any integer. Show that: if 1 < gcd(n,m) < m, then n 1R is...
Apr27-07 03:05 PM
1 1,467
Hi, What's the relationship between the image and kernel of T and the image and kernel of Tn? I think we saw in...
Jan14-05 09:52 PM
3 2,633
Hi all! Does anyone know a general method for determining the image of a lin map? Im aware of the definition if...
Nov24-08 08:50 AM
5 3,607
Well I have developed a number system which allows the existence of imaginary numbers. Please visit it at :...
Jun19-12 01:08 PM
14 4,942

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