Characteristic Definition and 287 Threads

Most definitions of "field" I've seen include the requirement 1≠0. One book didn't, and instead defined the "characteristic" of a field as the smallest non-negative integer n such that \sum_{k=1}^n 1=0 The books that include the requirement 1≠0 then go on to define an "ordered field", and...

Homework Statement This is question 30, section 2.5 from "Abstract Algebra 3rd edition" by Herstein. 2. Relevant information A subgroup H of group G is called characteristic if for all automorphisms phi of G, phi(H) is a subset of H. (I paraphrased this from question 29. I don't know...

The Euler Characterisitc can be computed from the dimensions of the Z homology of a space. Are there any other invariants that can be computed from the dimensions of the Z homology?

Homework Statement Let F be a field with order 2^n. Prove that char (F) = 2. Homework Equations The Attempt at a Solution My reasoning is that since a field is an integral domain, its characteristic must be either 0 or prime. After that I get confused, because would the char (F)...

so a charateristic function of a RV is complex valued funtion. from my lecture, the distribution funtion of a Random variable is not always "well behaved", may not have a density etc. A charateristic function on the other had is "well behave". What i don't understand is, is that the only reason...

I was wondering if sets A and B, with the following property: \mbox {Either } A\bigcap B=\emptyset \mbox{ or } A\bigcap B=A. have a special name. The name per se is not that important, however, what i am asking is whether these are well known/studied sets, or if they are of any special...

I have to find the absolute value of the transfer function for the circuit shown in the attachment. However, I have capacitors instead of inductors in my circuit and inductors instead of capacitors. So, the cross circuit will have L in the upper and lower branch and two C in the cross. I...

Homework Statement For each matrix A below, let T be the linear operator on R3 thathas matrix A relative to the basis A = {(1,0,0), (1,1,0), (1,1,1)}. Find the algebraic and geometric multiplicities of each eigenvalues, and a basis for each eigenspace. a) A =...

Homework Statement I'm working on a problem which is show that the matrix A = (^{a}_{c} ^{b}_{d}) is diagonalisable iff (a-d)2 + 4bc > 0 or a-d = b = c = 0 Homework Equations The Attempt at a Solution I've shown if (a-d)2 + 4bc > 0 then the characteristic polynomial has 2...

Homework Statement A is an nxn square, real matrix. Let f(x) be the characteristic polynomial, write f(x) = xn - c1xn-1 + ... + (-1)rcrxn-r + ... + (-1)ncn Show that cn-1 = \sum det (Aii) where Aii is the (i,i) minor of A. Similarly, what is the coefficient cr? Homework Equations...

Homework Statement Suppose A is a 2x2 real matrix with characteristic polynomial f(t) = t2 - 5t +4. Find a real polynomial g(t) of degree 1 such that (g(A))2 = A. Suppose A is a 2x2 complex matrix with A2 ≠ O. Show that there is a complex polynomial g(t) of degree 1 such that (g(A))2 = A...

Homework Statement http://img39.imageshack.us/img39/7496/59187398.th.jpg VDON=0,7 First it is asked to calculate V0 for Vin=-1V and Vin=-5V. Secondly it is asked to draw V0(Vin) for -10<Vin<10 Homework Equations The Attempt at a Solution Using Kirchhoff Volt Law I've...

Prove or disprove that function \phi(t)=\frac{1}{1+|t|} is charcteristic function of some random variable.

Homework Statement A is an nxn invertible matrix. Show that PA-1(x) = (\frac{(-x)^n}{det(A)}) *PA(1/X) Homework Equations det(AB) = det(A)det(B) The Attempt at a Solution Ok from what I understand this is the proof for the characteristic polynomial for the inverse of a...

First to tell, I'm a ordinary people who curious in science field. I can't use difficult word myself but I can understand when you use it don't worry. ......... Most of atom is space right? (Nucleus at center and electron cycle around very far away compare to it's size.) Okay, what I...

Let A be an n x n matrix. Show that det(A) is the product of all the roots of the characteristic polynomial of A.

Homework Statement How do I show that the cp is p(x)=x^n, dimA=n? Homework Equations A^k=0 for some k (obviously need to show k=n); p(A)=0 The Attempt at a Solution p(A)=0 <=> A^n + ... + det(A)=0

Homework Statement A characteristic property is a property that can be used to help identify a substance since it is the same for all samples of the substance. We have now studied mass, volume and density. Which of these is a characteristic property of substances? Explain. Homework...

"Consider a first order linear PDE. (e.g. y ux + x uy = 0) If u(x,y) is constant along the curves y2 - x2 = c, then this implies that the general solution to the PDE is u(x,y) = f(y2 - x2) where f is an arbitrary differentiable funciton of one variable. We call the curves along which u(x,y) is...

Hi PF readers, When trying to establish \lambda values by solving a characteristic equation (for simplicity of 2x2 matrix) can one produce solution that contains complex roots? If yes, what does that show about the eigenvectors? Thanks in advance! Cygni

Can anyone explain to me why each field of characteristic zero contains a copy of the rationals, or a subfield that's isomorphic...

Hi, I have Ids vs Vds characteristic curves for a MOSFET at Vgs = 2V and Vgs = 2.5V in both the linear (ohmic) and saturated regions. I wanted to try to figure out the threshold voltage for the MOSFET from this information only. I had two ideas of how to do this, but they differ by a factor...

Homework Statement I need to use MATLAB to solve these problems. http://users.bigpond.net.au/exidez/IVDP.jpg Homework Equations MATLAB The Attempt at a Solution a) R1=3.6; R2=R1; C1=33*10^-6; C2=22*10^-6; % defining the polynomial constants Vs=[R1*R2*C1*C2...

Hi. Does anyone know a good source for learning about the characteristic function of a joint pdf. Is there any nice rules for that? For example assume having a waiting time density and a jump density which are independent (easy things first). Is there an elegant way to get the characteristic...

Homework Statement Given two fields F,E with different characteristic. Prove or disprove the following statement: "Field homomorphisms between fields of different characteristic cannot exist" Homework Equations T : F1 --> F2 is a field homomorphism if 1) T(a+b) = T(a) + T(b) 2) T(ab)...

http://users.on.net/~rohanlal/qM.jpg I don't understand how this answer is obtained for the homogenous solution. What does characteristic equation in "r" mean and how does it help achieve the final solution of Asin(Wt) + Bcos(Wt)?

Hi, I am taking an online course on functional integration and the professor is introducing measure sets and characteristic functions. He introduced properties of characteristic functions and then gave us Bochner's Thm. which basically says that if a function satisfies the properties he...

Theorem 5.3: Let A be in M_n_x_n(F). (a) The characteristic polynomial of A is a polynomial of degree n with leading coefficient (-1)^n. (b) A has at most n distinct eigenvalues. Note: The theorem can be proved by a straightfoward induction arguement. Question: Can someone help with the...

Hi, there are a few questions and concepts I am struggling with. The first question comes in 3 parts. The second question is a proof. Question 1: Please Click on the link below :smile: Question 2: Please Click on the link below :smile: For Q2, could you please show me how to...

Are there any reference tables for what to use as the characteristic dimension of various shapes when calculating the Reynolds number? I am very interested in ballistics, and have done research and calculations for various ways of estimating the drag coefficient of various bullet shapes. I...

For the ODE x''+2x'+6x=sin2t what is the characteristic equation? Is it m^2+2m+6=0 or m^2+2m+6=cos2t

How do you determine a characteristic table with the given D-Flip Flop equation Q+ = X.Q + X'. Q' Also how do you use this flip flop and design a frequency divider. I am not really clear on these concepts. Can anyone help? I have attached my design of the circuit.

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?