Characteristic Definition and 307 Threads

I was reading about it here: http://mathworld.wolfram.com/CharacteristicFunction.html very neat. But then I tried out of boredom integrating the expression by parts where u = the exponential term and v = f (x) (or P(x)). The integral came out nicely as I got a term similar to the left hand...

C(a,b) = a^2 + ab -b^2 The characteristic value of a Fibonacci sequence is an interesting property. 1) C(a,b) = C(a,a-b) 2) C(a,b) * C(c,d) = C(ac+ad-bd,bc-ad) 3) C(a,b) * C(a,a-b) = C(2a^2-2ab+b^2,2ab-b^2) =(C(a,b))^2 C(a,b)^n = C(A_{n},-B_{n})...

The characteristic function of the RATIONALS is a well-known example of a bounded function that is not Riemann integrable. But is the characteristic function of the IRRATIONALS (that is, the function that is 1 at every irrational number and 0 at every rational number) Riemann integrable on an...

Hi there, i have this problem: I have a sinewave signal contaminated by a large amount of noise. I already know the phase of the signal and its characteristic frequency, and I am searching for its magnitude. If I do a basic Fourier transform, I would obtain the magnitude at its...

Hello, I understand the current concept of the characteristic however there either is a mistake in my answerbook or I made a mistake log15 850 = 850(1/15) = 1.568 The characteristic should be 1 and the mantissa is 0.568 -- My answer book says it's 2. I have done all my other exercices...

Is it possible to exactly derive the mode of a probability distribution if you have the characteristic function? I cannot get the pdf of the distribution because the inverse Fourier transform of the characteristic function cannot be found analytically. Any thoughts would be appreciated...

I know the process of their production, now I want to know what's their origin? How does an atom produce them? PS:Donno whether it's the right forum to ask this question or not, so feel free to move it to the right place!:smile:

Let G=Z_2XS_3 (Z_2:cyclic group of order 2; S_3: Symmetric group on 3) . Show Center of G, Z(G) is not a fully characteristic (or invariant) subgroup of G. Apparently, Z(G)=Z_2 I know that I need to show that there exists an endomorphism g from G to G such that g(Z_2) is not contained in...

Homework Statement Given an nth order linear homog. diff eq. how can I find the solution for its nth degree characteristic eq? I know its simple Algebra but please help. if possible please give a 5th deg eq. thx

Homework Statement Show that any field of characteristic 0 is perfect. 2. The attempt at a solution Let F be a field of characteristic 0. Let K be a finite extension of F. Let b be an element in K . I need to show that b satisfies a polynomial over F having no multiple roots. If f(x)...

Homework Statement Let (X,d) be a metric space, A subset of X, x_A: X->R the characteristic function of A. (R is the set of all real numbers) Let V_d(x) denote the set of neighbourhoods of x with respect the metric d. Prove that x_A is continuous in x (x in X) if and only if there...

Hi everyone Books mention the Open Circuit and Short Circuit tests on a synchronous generator in order to determine its synchronous impedance. One observes that the Short Circuit Characteristic (plot of short circuit armature current versus field current) is a straight line all the way...

Homework Statement im trying to find the characteristic equation of a circuit with a current source and 3 elements all in parallel: a resistor and 2 inductors L1 and L2. Homework Equations i believe the current can be calculated as: i(t) = v(t)/R + iL1(t) + iL2(t) The Attempt at a...

Is it true that the characteristic polynomial of an n by n matrix over GF(q) splits into linear factors over GF(q^n)? I see that it must do if the polynomial is irreducible but what if it isn't?

Homework Statement If A is a 6x6 matrix with characteristic polynomial: x^2(x-1)(x-2)^3 what are the possible dimensions of the eigenspaces? The Attempt at a Solution The solution given is that, for each each eigenspace, the smallest possible dimension is 1 and the largest is the...

Homework Statement Recall that a subgroup N of a group G is called characteristic if f(N) = N for all automorphisms f of G. If N is a characteristic subgroup of G, show that N is a normal subgroup of G. The attempt at a solution I must show that if g is in G, then gN = Ng. Let n be in N...

Homework Statement I am in such a situation, where we are trying to measure the characteristics of a stepping motor in order to verify its operational characteristics. I have tried measuring the motor's torque in many ways but I am having trouble following the company maker's method given...

Main characteristic of the JK flip-flop stands for... What is "main characteristic" referring to?

Homework Statement Hi, I have the following circuit: http://i137.photobucket.com/albums/q208/infinitbelt/ProblemSet3Circuit1.png" Also, the following is known: X=60 V R1= 10 Ω R2= 20 Ω R3= 10 Ω R4=5 Ω R5=20 Ω R6 = 5 Ω Homework Equations V = IR y = mx + b The...

Hi, I have the following circuit: http://i137.photobucket.com/albums/q208/infinitbelt/ProblemSet3Circuit1.png" Also, the following is known: X=60 V R1= 10 Ω R2= 20 Ω R3= 10 Ω R4=5 Ω R5=20 Ω R6 = 5 Ω How do I go about finding a V-I characteristic of this circuit? I know that the...

Homework Statement Okay, so this is a three-part question, and I need some help with it. 1. I need to show that the function f(x) = e^{-1/x^{2}}, x > 0 and 0 otherwise is infinitely differentiable at x = 0. 2. I need to find a function from R to [0,1] that's 0 for x \leq 0 and 1 for x...

Homework Statement If I have a n x n matrix B, and I must show that a vector a is an eigenvector for the matrix B and I have to find the corresponding eigenvalue, what is the easiest way of doing this? The Attempt at a Solution I know I can find the characteristic polynomial, but I thought...

[SOLVED] urgent: effect of light on IV characteristic of pn junctions ^ ^;; Last resort time, needs to be answered by 4pm today. (18/01/08) It's a pretty qualitative question, and if possible I'd like a qualitative answer. The reason for this is that this is only a weekly experiment I've...

A true statement: Two similar matrices have the same characteristic polynomial. The converse however is not true in general: two matrices with the same characteristic polynomial need not be similar. HOw can I prove this? Any help appreciated.

Haven't been able to find the answer anywhere IRL yet, so I thought I'd see if someone in the PhysicsForums could help me with this one. When doing SEM/EDS (EDX/EDXS) (~equivalent to x-ray fluorescence) analysis it looks as if my europium containing samples contain copper as well, which'd...

If I am using the method of characteristics to solve a PDE \Psi(x,t) (first order, semi-linear), and after using the method of characteristics I find that the Jacobian |\frac{\partial{(x,t)}}{\partial{(\sigma,\eta)}}| = 0 (where \sigma and \eta are parameters for the curve) does this imply...

This is something I've been trying to work on on my own for the past few days but I'm not sure how to approach it. My Question: a. Let E be a Galois extension of a field F with characteristic 0. Prove that there is a unique smallest subfield K such that F \subseteq K \subseteq E , K is...

Good morning lovely people ! As I got some really helpful advice here yesterday i though i'd try it again, hopefully you haven't yet had too much from me (-: So my question is concerning the attached PDF file (Last problem #3) i am asked to find the current I_B in 3a) and 3c) but to my...

Why do you guys think that given two 3x3 matrices, they are similar if and only if their characteristic polynomial and minimal polynomial are equal (this reasonably fails for 4v4 matrices though)?

What is the definition of a characteristic of a ring? Is it the smallest n such that n1=0? or is it the smallest n such that nr=0 for all r in R.

Homework Statement The K characteristic X-ray line for tungsten has a wavelength of 1.94 10-11 m. What is the difference in energy between the two energy levels that give rise to this line? Express this in each of the following units. (a) joules J (b) electron volts eV Homework...

Hi, Why is it that if A is m×n-matrix and B is n×m matrices such that m<n, then AB is m×m and BA is n×n matrix. Then the following is true: pAB(t) = t^(m-n)*pBA(t) where pAB(t) and pBA(t) are characteristic polynomials of AB and BA thanks

In "Dr. Euler's Fabulous Formula" by Paul Nahin, early in chapter 1 is discussed characteristic polynomials of a square matrix and the Cayley-Hamilton theorem, that any square matrix A satisfies its own characteristic equation. On page 21 it states p(lambda) = lambda^2 + a1*lambda + a2 = 0 and...

Why is the characteristic of a finite field a prime number?!

And again a question: L is a field for which a \in L . The matrix A = \frac{1}{2}\left( {\begin{array}{*{20}c} 1 & 1 & 1 & 1 \\ 1 & a & { - 1} & { - a} \\ 1 & { - 1} & 1 & { - 1} \\ 1 & { - a} & { - 1} & a \\ \end{array}} \right) has the characteristic polynomial x^4 -...

The Rindler geometry and its horizon can be obtained by a simple succession of Poincaré transformations to match the frame of an accelerated observer. By combining this SR result and the equivalence principle it follows that a uniform gravitational field is represented by the Rindler metric and...

Hi all, Im currently researching into Multivariate distributions, in particular I am trying to derive the characteristic function of the bivariate distribution of a gaussian. While knowing that a gaussian density function cannot be integrated how is it possible to find the characteristic...

Let's say I'm given a DEQ: (1) y^{(n)}+a_{n-1}\cdot y^{(n-1)}+\ldots + a_{0}\cdot y=0, where y is a real function of the real variable t, for example. I could now rewrite this as a system of DEQ in matrix form (let's not discuss why I would do that): (2) x'=Ax,\quad x=(y,\ldots,y^{(n-1)}). If I...

Prove: Similar matrices have the same characteristic polynomial. By characteristic polynomial of A i mean det(A-tI) where t is a scalar. A is similar to B if A = Q^-1 B Q for some invertible matrix Q. (i.e. B is the matrix representation of the same linear transformation as A but under a...

I'm in graduate analysis this year, but I've been out of school as a teacher for 6 years so I'm a bit rusty. Any help would be appreciated on this simple question. My apologies for not knowing the Math-type. Yesterday in class we were discussing an example which demonstrated the...

Hi! What can be said about the intensity ratios of characteristic X-rays (Kalpha to Kbeta ) originating from a X-ray tube? I mean roughly and in general, not for some very specific anode material. I first thought that K-L (Kalpha) transitions would be more likely to happen than K-M:s...

"Let m_T(x), f_T(x) denote the minimal and characteristic polynomials of T, respectively. Let k be a scalar. Show that m_{T-k}(x) = m_T(x+k) and f_{T-k}(x)=f_T(x+k)." I was able to show that the minimal polynomials were the same. But my argument was based on the minimality of the degree of...

"Let T be a the transformation on V = C^3 given by the equation T(x)=-y-2z T(y)=3x+5y+7z T(z)=-2x-3y-4z where (x,y,z) denotes the standard basis. Find the eigenvalues of T and the corresponding eigenspaces." Is there a way to find the eigenvalues without solving the 3 equations? How...

Hi, I'm a little stuck on this problem. The question is: Let T be a linear operator on a two dimensional vector space V , and suppose that T \neq cI for any scalar c. (here I denotes the identity transformation). Show that if U is any linear operator on V such that UT = TU ...

This kind of bothers me: our textbook does not explain (and the professor either) where characteristic function comes from, all it says is what it defined as, which is E[ejwX], where E is expectation of random variable X. But where is this e-term coming from? Thanks in advance.

Characteristic Line of a Sound Wave?? Okay, I have another fluids question: The velocity (u) caused by a rightward propagating wave in a gas is described by the nonlinear wave equation (du/dt) + [a + ((gamma+1)*u/2)]*(du/dx) = 0, where a is the speed of sound, gamma is a constant, and...

y^(7)-y^(6)-2y^(4)+2y^(3)+dy-y=0 Note: There is exactly one real zero of the characteristic polynomial and it has multiplicity 3 (it is a positive integer!). The other zeros are complex and they have multiplicity 2. Sadly I missed this lecture day, and am unsure of where to start. Any...

"property" vs "characteristic" OK, semantic hair-splitting time. The two words "property" and "characteristic" mean essentially the same thing, but they are often distinguished from each other in textbooks. For example, with waves there are two sets of attributes (yet another synonym) "the...

So, I have stared at this for a while: Notation: Q' - inverse of Q, != stands for "not equal"; Suppose A and B are nxn matrices such that A = QBQ' for some invertible matrix Q. Prove that A and B have the same characteristic polynomials I can prove that they have the same determinant, but...

Hi Guys: My question is this for the circuit in the 1st fig: sketch the transfer charcteristic "vo" versus "vI" the answer of this question is the 2nd fig. but i want to know that what is the logic behind this sketch or in other words how we can draw such a sketch. Thanks in advance