Positive Definition and 964 Threads

I ran into an infinitely dimensional matrix and wanted to show it is positive definite. I think I cannot do so by checking the principal minors as for finitely dimensional matrices... Can someone let me know how to show its positive definiteness? Thanks a ton!

Homework Statement Assume that f is a differentiable function such that f(0)=f'(0)=0 and f''(0)>0. Argue that there exists a positive constant a>0 such that f(x)>0 for all x in the interval (0,a). Can anything be concluded about f(x) for negative x's? Homework Equations The...

I was trying to prove the following but couldn't succeed. Is there a systematic methods to prove that the following infinite sum is positive? (alternating series) sum from n = 0 to ∞ of ((-1)^{n}* x^{n+z}) / (n+z)! conditions x≥0 and z≥1 note: when x≤1, we can directly see that s_{n}-...

I want to understand positive operator valued measures in QM, in particular why they are considered "observables". Anyone know a good place to start reading about this? I know some functional analysis and some measure theory, but I haven't made it all the way to the spectral theorem.

Firstly, the set E is defined: "Let E be the set of all positive real numbers t such that tn<x." Later on the proof goes: "Assume yn>x. Put k=yn-x / nyn-1. Then 0 < k <y. If t ≥ y - k, we conclude that yn-tn ≤ yn-(y-k)n < knyn-1 = yn-x. Thus tn>x, and t is not a member of E. It follows...

Homework Statement A particle has displacement x(t) = (t^3 - t^2)e^-t for times 0=<t=<9. Find its velocity v(t) and determine for what times the particle is moving in the positive x direction. Homework Equations Differentiating x(t) you get v(t)=-t(t^2-4t+2)e^-t The Attempt at a...

I don't know where to ask this question, but anyways, since it was asked in an exam, so finding out the correct answer afterwards is a moral responsibility as a homework. So here I am. My question is whether the compound 2-Hydroxy-5-nitrobenzaldehyde (Did I named correctly?) gives positive...

I am not a student of Physics. I want to know. I am curious. I never understood a basic thing. What is the difference between a positive and a negative electrical charge? What characteristics describe the two charges? Are they just something you mug up as a given example of the duality in the...

Homework Statement Decide for or against the positive definiteness of [2 -1 -1 -1 2 -1 = A -1 -1 2] [2 -1 -1 -1 2 1 = B -1 1 2] [5 2 1 2 2 2 = C 1 2 5] Homework Equations Each of the following tests is a necessary and sufficient condition...

Hi I know that the sphere has positive curvature everywhere, and the torus has positive an negative curvature. Is there a space homeomorphic to the sphere such that this space has negative curvature everywhere? And, is there a space homeomorphic to the torus such that the curvature is always...

Is there a way within reasonable errors to say what part of the positive integers are prime and what part is factored greater than one? Oh course one is a factor of all numbers greater than zero. Yeats ago playing around a floating constant became known to me. to the tenth decimal place is...

I have calculated magnitude of acceleration of an object slowing to a stop to be: -5.1m s^-1. I then had to find the magnitude of the unbalnced force applied to the object for it to stop which i found to be: So F= 1500 kg * 5.1 m s^-2 Which equals 7650kg m s^-2 Which...

Hi, Is there any method(circuit) to retain only the positive frequency components of a signal? thanks in advance.

Homework Statement Determine the set of positive values of x that satisfy the following inequality: (1/x) - (1/(x-1)) > (1/(x-2)) a) (0, 1) union (2^1/2, 2) b) (0, 1/2) union (1, 2) c) (1/2, 1) union (2^1/2, 2(2^1/2)) d) (0, 2^1/2) union (3/2, 2) e) (1, 2^1/2) union (2, 2(2^1/2))...

Homework Statement f(x)= 3+6x-2x^3 (a) Determine the values of x for which the graph of f has positive gradient (b) Find the values of x for which the graph of f has increasing gradient Homework Equations I had originally thought the two terms meant the same thing, but when I checked the...

Homework Statement Prove that if limXn = +∞ and limYn>0 then limXnYn=+∞ The Attempt at a Solution limXnYn = limXnlimYn = (c)(+∞) where c is a positive real number I know in my head that a positive number multiplied by infinity is positive, but I am unsure how to prove this and we have...

So earlier this year I came here to discuss about having fun with groups, rings and isomorphisms and such. I fell upon the idea of finding an isomorphism of the positive rationals to the sequence of the exponents found in their prime factorization. I didn't know what much to do with it since I...

Homework Statement You are moving into an apartment and take the elevator to the 6th floor. Does the force exerted on you by the elevator do positive or negative work when the elevator (a) goes up and (b) goes down? Explain your answers. Suppose your weight is 685N and that of your...

There is a link to a picture below. It shows two Hydrogen atoms on the same side of an Oxygen atom (both on the lower half of the Oxygen atom). Because the distribution of Hydrogen in H2O is not symmetrical, does that mean that, on average, the H2O molecule is more negatively charged in its...

Homework Statement Consider the following convergent series. Then complete parts a throw d below. sum[k=1,inf] 5/k^7 a. Find an upper bound for the remainder in terms of n Homework Equations Estimating Series with Positive Terms Let f be a continuous, positive, decreasing...

"Positive Set" in an Ordered Integral Domain I'm currently reading Durbin's Modern Algebra, and I have a question about the positive set in ordered integral domains. Durbin characterizes an ordere integral domain as one with a subset which is closed to addition and multiplication, and...

Homework Statement I created a program that will calculate the factorial of the number entered and am having a hard time getting it to not accept decimals or fractions.#include <iostream> using namespace std; int main (){ int q=0; int number = 0; cout<<"Please enter a positive whole...

I think it's a pretty simple question. Let's say we're talking about a moving elevator in which a person stands on a digital balance. The textbook tells me to treat the downward direction as positive, so the value of acceleration is 9.8 m/s^2 instead of -9.8m/s^2 I'm asked to find out the...

Homework Statement If vector a is added to vector b = 7.4i + 7.7j, the result is a vector in the positive direction of the y axis, with a magnitude equal to that of vector b. What is the magnitude of vector a?Homework Equations The Attempt at a Solution (Is the vector in the positive direction...

Homework Statement "True or false: there is a smallest positive number. Explain."Homework Equations N/A, but for practice I'll try my hand at phrasing it mathematically: \forallx\in(0,∞)\existsz\in(0,∞):(z<x)The Attempt at a Solution My issue with the question is mathematically proving it - I'm...

I never could get leyden jars to work. I'm trying to use a few 3 liter bottles I have here at home. I also have quite a few solar panels and other materials like aluminum foil and copper. I was thinking today that it seems it would be easier to have 2 bottles, 1 with a copper lead dipping...

Homework Statement find the positive integers k for which lim x->0 sin(sin(x))/x^kHomework Equations exists, and then find the value of the limit The Attempt at a Solution I did the first three k's k=0 lim x->0 sin(sin x))/x^0= 0 undefined k=1 lim x->0 sin(sinx))/x^1= 1 k=2 I might be...

Homework Statement Two blocks attached by a string slide down a 17 incline. The lower block has a mass of 0.2 kg and a coefficient of kinetic friction of 0.2. The upper block has a mass of 0.9 kg and a coefficient of kinetic friction of 0.9. Find the magnitude of the acceleration of the...

Homework Statement In a stage production of Peter Pan, the 63 kg actress playing Peter has to fly in vertically, and to be in time with the music, she must be lowered, starting from rest, a distance of 2.6 m in 2.2 s. Backstage, a smooth surface sloped at 58 supports a counterweight of...

Let's say you have 2 charges of magnitude 2C except 1 is + and the other -. They're separated by 2m. dipole moment=p=qL Which q do you plug in there?

Hi, i was wondering is there a way I can find the eigenvalues of a positive definite matrix. ?

Homework Statement find the magnitude and the angle that it makes with the positive x-axis? http://imageshack.us/photo/my-images/594/unledzmo.png/ Homework Equations The Attempt at a Solution The answer that I have is F= 179.37 at an angle of 91 degrees. Am I right? I took F1...

Homework Statement For the oscillatory solution (+k2) solution, suppose x is restricted to 0\leqx\leqa by requiring \psi(x)=0 and \psi(a)=0, what are the restrictions on A,B and k? Homework Equations given \psi(x)=Acos(kx)+Bsin(kx) The Attempt at a Solution so, I pretty just...

Homework Statement Let A be a positive definite n\times n real matrix, b\in\mathbb{R}^n, and consider the quadratic polynomial Q(x)=\frac{1}{2}\langle{x, Ax\rangle}-\langle{b, x\rangle}. Show that Q is bounded below. 2. The attempt at a solution I have to come up with a constant m so that...

A=2i-10k give the angle that A makes with the positive x-axis ? do i need to make x axis=i and i go A.B/AxB ?

Homework Statement \foralla \inA\existsb\inB(a\inC \leftrightarrow b\inC). Homework Equations The Attempt at a Solution\forall This is equivalent to \existsa\inA\neg\existsb\inB(a\inC \leftrightarrowb\inC). Homework Statement

Is Zero a positive or negative whole number ? Is it even a whole number ?

Homework Statement Three equal positive point charge of magnitude Q=7.00uC are located at three corners of a square of edge length d=4.8cm. A negative charge of -21.00uC is placed on the fourth corner. A) At the position of the negative charge, what is the magnitude of the electric field due...

Identify which of the ff. object will be positive or negative charge 1) Hand and Hair 2) PVC and Tetlon 3) Glass and Poly ester 4) Rubber and rubber 5) Hand and wood

What is positive and negative eigenspaces? Can you recommend me a referance to know them?

I was having a discussion about thermal insulation (high temperature) and I thought that positive pressure (meaning the heat is being blown onto the insulation) would reduce how effective the insulation was. Say a 1/2" of insulation reduced temperature from 1000 degrees F to 500 degrees F...

Homework Statement Given a circular wire with radius R. Choose the origin in the center of the circle, the z-axis perpendicular to the circle. One halve of the circle contains a positive line charge \lambda, the other halve a negative line charge of the same magnitude. (a) Sketch the electric...

I'm designing a portable device running off of 2 AA batteries that requires positive both positive and negative 5v power at the same time. What is the best/cheapest way to achieve this?

Homework Statement Show that in this set-up, the potential at a generic point (-x, 0, 0) (for x positive) is zero: two point charges placed at (-a, 0, +a) and (-a, 0, -a) the mirror charges are (a, 0, +a) and (a, 0, -a) The Attempt at a Solution V=(q/(4 pi epsilon0)) ((1/(sqrt((x^2...

what is charge? i know that it is of two types positive and negative, i need the physical interpretation and it would be really helpful if anyone can tell something about the history of discovery of charge,well i know about the discovery of electrons and all that ,what i am interested in...

Homework Statement Give a big-O estimate of the product of the first n odd positive integers. Homework Equations Big-O notation: f(x) is O(g(x)) if there are constants C and k such that |f(x)| ≤ C|g(x)| whenever x > k. The Attempt at a Solution The product of the first n odd integers can be...

Can a charge, brought into a chargeless world filled with some geometry of conductors and dielectrics, induce a negative potential anywhere in that world? I feel the answer is no. But I cannot think of a good way to prove it, or even attack the problem. More explicitly, imagine a world...

Homework Statement 2 part problem. I've already solved the first part. Two parallel plates are held at potentials of +380.0 V and -150.0 V. The plates are separated by 3.00 cm. a. Find the electric field between the plates. b. An electron is initially placed halfway between the...

I would like to have a function f such that f(0) = 0 and f(x) = 1 for any x>0. I can compute f in the following way: f(x) = (2*x+1)/2 - (2*x-1)/2 . Here the division is integer division. But if x=0, here we divide (2*0-1)/2 or -1/2, which is a problem. Because we do not have any number -1...

Homework Statement How much positive and negative charge are in a 50g Tungsten ring? Homework Equations Standard atomic weight 183.84 The Attempt at a Solution