Characteristic Definition and 307 Threads

Homework Statement 1)Prove that the characteristic roots of a hermitian matrix are real. 2)prove that the characteristic roots of a skew hermitian matrix are either pure imaginary or equal to zero. Homework Equations The Attempt at a Solution

Homework Statement Given characteristic functions f and g on the intervals [1,4] and [2,5] respectively. The derivatives of f and g exist almost everywhere. The integration by parts formula says \intf(x)g'(x)dx=f(3)g(3)-f(0)g(0)-\intf'(x)g(x)dx. Both integrals are 0 but f(3)g(3)-f(0)g(0) is...

I am trying to compute the inverse Fourier transform numerically (using a DFT) for some complicated characteristic functions in order to compute their corresponding probability distribution functions. As a test case I thought I would invert the characteristic function for the simple exponential...

Homework Statement B = |a 1 -5 | |-2 b -8 | |2 3 c | Find the characteristic polynomial of the following matrix. Homework Equations None The Attempt at a Solution So basically I have to find the det(B-λI). No matter what I do to the matrix I can't make the...

Hi: There are 3 invariants. The first one is a trace. The third one is a determinant. So they are invariants. The strange thing is the 2nd one. It is a hybrid term. Why is it also an invariant?

Let V =Mn(k),n>1 and T:V→V defined by T(M)=Mt (transpose of M). i) Find the minimal polynomial of T. Is T diagonalisable when k = R,C,F2? ii) Suppose k = R. Find the characteristic polynomial chT . I know that T2=T(Mt))=M and that has got to help me find the minimal polynomial

Hello physics forum, I'm running an experiment where characteristic x-ray are produced from an Iron sample, and I was just wondering if these x-rays are emitted in any random direction, or is there a "favored" direction they can be emitted in? Thank you in advance. Neville.

According to the Brønsted-Lowry definition, a base is a compound that can -keyword- accept H+, and an acid anything that can give H+.

Homework Statement Let f(x,y) be the soloution of xu_x +yu_y = u^4 that is defined in the whole plane. Prove that f = 0 . Hint: Think of the characteristic curves of this PDE. HOPE You'll be able to help me Thanks in advance! Homework Equations The Attempt at a Solution...

I have been thinking about this for quite some time now. When I look at the function that descibes the fat cantor set namely: f(x) = 1 for x\inF and f(x) = 0 otherwise, where F is the fat cantor set. I wonder, how do I prove that this is non-riemann integrable? I have considered...

Is there an example of a real vector bundle over a compact smooth manifold with all zero characteristic classes (Euler class,Stiefel-Whitney classes and Pontryagin classes) that is non-trivial?

hii... you all know about IV Characteristic PIN diode.. I fabricate PIN diode and want to analysis my result.. what is the forward voltage drop for PIN diode? are the voltage fix o variable.. ??

Homework Statement Prove the statement that (a,b) = (c,d) iff a = c and b = d with only using the first order logic (rules), the axiom of extensionality, the axiom of pair, and the definition that (a,b) = {{a},{a,b}}. Any intuitive approach should be avoided. The example of intuitive proof...

Hi there, Recently I have come across a proof with application of characteristic function. After some steps in the proof, it concluded that there is a neighborhood of 0 such that the characteristic function is constant at 1, then it said the characteristic function is constant at 1...

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...

Homework Statement Let V=C^4 and consider the linear map V->V given by the matrix: {{12,-6,6,-6},{2,21,21,51},{-3,12,12,30},{1,-9,-9,-21}} (Each {...} denotes a row, tried to use Latex but got extremely confused!) Given that chA(X)=(X-6)^4, calculate: (i) The power such that...

Homework Statement Three beads of equal mass m are constrained to lie on a circular hoop of radius a = 1. The beads are connected by identical springs of spring constant k. The equations of motion for displacements are (I am going to use x, y, and z, where x = theta 1, y = theta 2, z =...

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...

I know zero about the characteristic classes of finite group representations and would appreciate a reference. specifically, if I have a faithful representations of a finite group,G, in O(n) what can I say about the induced map on cohomology, P*:H*(BO(n))-> H*(BG) ? I am mostly interested in...

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...

Homework Statement Hiya, I was looking over a General Relativity paper today, and at the end of a question on Geodesic Deviation, was "Give a brief statement of a physical effect or thought-experiment which illustrates how the time sqrt(R/g) characterises the Earth’s gravity." (R is the...

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.