Positive Definition and 963 Threads

Homework Statement can an object have a positive velocity and a negative displacement? can an object have a negative velocity and a displacement of zero? can an object have a value for distance and an average speed of zero? PLEASE EXPLAIN EACH CASE TO ME! PLEASE LOL :P Homework...

Homework Statement Let E be the exchange matrix (ones on the anti-diagonal, zeroes elsewhere). Suppose A is symmetric and positive definite. Show that B = EAE is positive definite. Homework Equations The Attempt at a Solution I've tried showing directly that for any conformable vector h...

URGENT: Can you prove or disprove: Let A and B be (complex matrices) positive definite with trace 1. Given A < B, (B-A is pos def ) then A^2 < AB (AB-A^2 is pos def)

Homework Statement This is the equation where i, a, b and c are positive integer. http://www.icedsolo.com/eq.GIF Homework Equations http://www.icedsolo.com/eq.GIF The Attempt at a Solution The question is, proof whether K is always positive, or it is positive in certain range of a, b, and...

Can anybody explain what is meant by positive definite Hamiltonian? All I know is that if a Hamiltonian can be factorized as H={Q}^{\dagger}Q then that Hamiltonian is one such example. But I am not sure if that is the definition of a positive definite Hamiltonian. In the quantum mechanical...

Homework Statement I took 2 plots. Can someone explain to me why the first one comes out positive and second negative? Homework Equations The Attempt at a Solution

Hello there, This is my first post on this forum so bear with me if I don't know the rules or I am posting in the wrong area. I am coding up an of equation for a scattering rate which involve quite a few positive (and a couple of negative) exponentials which often have terms that go into...

From "The Theory of Groups" by Rotman 2.5. Prove that the multiplicative group of positive rationals is generated by all rationals of the form: \frac{1}{p}, where p is prime. ... um... no it's not. Right? How can I prove this when I don't even think it is true? I mean, for example take...

Homework Statement Let A and B be nxn positive self-adjoint matrices such that for all x \in Cn, x*Ax = x*Bx. Prove that A = B. Equivalently, prove that if A, B are positive operators on H such that <Ax,x> = <Bx,x> \forall x \in H, then A = B. Hint: See Lemma 2.12. Homework Equations...

Homework Statement Let T be a positive operator on a Hilbert space H. Pick an orthonormal basis {e1,e2,...,en} for H. Let A=[aij] be the nxn matrix representation of T with respect to the basis {e1,e2,...,en}, so that Tej=\sumaijei, j=1,2,...,n. (The summation is from i=1 to n; I'm not...

hi all, i was studying modulus when i came across this mod(xy) = modx mod y we consider 3 cases whereby both positive , both negative, or positive negative it reads here if we consider x and y to be negative it will be something like this mod xy = xy = - mod x ( - mod y ) = mod x mod...

The following two main principles are the very significant and positive result of the Michelson-Morley Experiment: 1. The laws by which the states of physical systems undergo changes are not affected, whether these changes of states are referred to the one or the other of two systems of...

what's the maximum area of an equilateral triangle that can be drawn on a positive curvature?

given acceleration a = 1 + ln x i can find that \Delta v^2 = 2xlnx and since it is given that when t = 0, x = 1,v = 0 \therefore v^2 = 2xlnx however i have been asked to prove v > 0 \; when \;t > 0 and i have no idea how to explain it in mathematcial terms, can anyone please give any suggestion?

The difference between two positive numbers is 3. The difference between their reciprocals is 1/90 What are the two numbers? I worked out that: x-y=3 and 1/x-1/y= 1/90 Is that right so far?

Let K\subseteq\mathbb R is a compact set of positive Lebesque measure. Prove that the set K+K=\{a+b\,|\,a,b\in K\} has nonempty interior.

Given a linear operator A, why is \sqrt{A^*A} positive? Where A* is the adjoint.

Homework Statement I need to find a positive REAL value x such that \frac{2-(4+x^2-x\sqrt (4+x^2) \sqrt (\frac{2+x^2+x\sqrt 4+x^2 }{8+2x^2})}{4\sqrt (4+x^2) } == 0 x cannot be complex or zero! So far, I don't even think its possible. Any suggestions? Homework Equations The Attempt at a...

This is a simple wording confusion. On one question that I did, the property for a positive focal length image was Real, Diminished and Inverted. On another question of the same type, the property for a positive focal length image was Real, Inverted and Smaller. So, my confusion is the...

[SOLVED] Positive Definite Matrices Homework Statement a) If A is Symmetric show that A-λI is positive definite if and only if all eigenvalues of A are >λ, and A-λI is negative definite if and only if all eigenvalues of A are <λ. b) Use this result to show that all the eigenvalues of...

[SOLVED] Positive Definite Matrices a) If A is Symmetric show that A-λI is positive definite if and only if all eigenvalues of A are >λ, and A-λI is negative definite if and only if all eigenvalues of A are <λ. b) Use this result to show that all the eigenvalues of [ 5 2 -1 0] [ 2 5 0...

Lot of people are telling negative sides career as a physicist, But it physics really in such a bad position? I had a wish to research on high energy physics(particle) . Now i am undergraduate student student of physics major. Should i change field at graduate study? or take risk? If i change...

[SOLVED] A limit Homework Statement How do you show that \lim_{x\rightarrow a}\frac{e^{-a^2/(a^2-x^2)}}{(a^2-x^2)^{2m}(x-a)}=0 for 'm' a positive integer and 'a' a real number >0??This is a type 0/0 indeterminate form but l'Hospital's rule is not helpful because when you differentiate the...

Homework Statement Prove that for all x there exists and x if it is an element of the positive integers, then there is an integer y and an integer z. Homework Equations The Attempt at a Solution I know that the contrapositive would be "If there is not an element of the positive...

Homework Statement An ion is accelerated through potential diff. of 250 V, directly perpendicular to mag. field. Find radius of the path of the ion in the field. Given: mass (m)=2.5 x 10^-26 charge(q)= 1.6 x 10^-19 Volts= 250 V Mag. Field (B) = 0.50 T Homework Equations...

Homework Statement The task is to show that the eigenvalues of overlap matrix \tilde S are positive. Homework Equations The overlap matrix is defined as (\tilde S)_{nm} = \langle \xi_n \vert \xi_m \rangle , with \xi_k being the base vectors of the wavefunction...

Homework Statement In the problem sin-1 is 59.1. I have to give it from the positive x axis. Homework Equations The Attempt at a Solution Would it be 360-59.1? or 180-59.1? Thank you very much

Homework Statement What are the x and y components of a vector a in the xy plane if its direction is 230° counterclockwise from the positive direction of the x-axis and its magnitude is 2 m? Homework Equations The Attempt at a Solution My main issue is I'm not sure where...

Problem: Suppose that {a_{k}}^{\infty}_{k=0} is a bounded sequence of real numbers. Show that \suma_{k}x^{k} has a positive radius of convergence. Work: I have attempted to use the ratio test and failed. I am suspicious I can try the root test, but I am not sure how to work it...

Hello, I was asked to write a C program to find minimum normalized positive number that can be represented in my computer. I know that the value is 2.2250738585072014e-308. I wrote the program to find the machine precision. Now i need to make some parameter changes to this program to find the...

Homework Statement The infinite series defined by \Sigma a_{n}, with a_{n}>0 are convergent. If then the series defined by \Sigma a_{n}^{2} coverges, prove it! Homework Equations The relevant equations has been stated above. The Attempt at a Solution Since every term in the first...

Homework Statement Determine all positive rational solutions of x^y=y^x.Homework Equations The Attempt at a Solution Obviously, x=y will always work. I think that is the only solution. If I can show that x^y must be rational, I think it will be easy because then both x and y must have the same...

have a matrix: X1+X2+X3+X4 = 0 X1+X2-X3-X4 = 0 X1-X2+X3-X4 = 0 the solutions that are formed are: t -t -t t Now i understand that they just used t to label the free variables.. but Iam not sure how they were able to tell which were negative and positive.. I tried to do it out, but...

[SOLVED] Showing exp is positive... ... well not quite. This isn't actually homework, but here's what I'd like to prove: \forall n \in \mathbb{N} : \sum_{k=0}^{2n}\frac{x^k}{k!} \ge 0. I tried going about it through induction, but got into trouble quite early on: I couldn't prove that...

Homework Statement Find the smallest number with 28 positive divisors. 28 = 14*2 or 7*4. So, it is either 2^13*3 or 2^6*3^3, right? Because 2^7 is manifestly larger than 3^2, it the latter, correct?Homework Equations The Attempt at a Solution

Q: Suppose q(X)=(X^T)AX where A is symmetric. Prove that if all eigenvalues of A are positive, then q is positive definite (i.e. q(X)>0 for all X not =0). Proof: Since A is symmetric, by principal axis theorem, there exists an orthogonal matrix P such that (P^T)AP=diag{c1,c2,...,cn} is...

Homework Statement prove that if lim_{x\rightarrow c} f(x) = L, then there are positive numbers A and B such that if 0 < |x-c|< A, then |f(x)|< B 2. The attempt at a solution i know it's something to do with the limit definition, where for \epsilon > 0, there exists a \delta > 0 such...

The problem is The limit as x approaches pos infinity ln(square root of x + 5) divided by ln(x) In the numerator only x is under the square root. I'm having trouble getting to this answer. If someone can take a look I would really appreciate it.

Help! Please I am trying to write a Lisp program to calculate the sum of the first N positive integers where, for example, when N = 6 the sum of the first N = 21 Any Ideas?

one of the "maths challenge" questions. one of the only ones i couldn't do :S I've tried for a good number of hours, but havnt found a way to do it. I feel any more time would just be brute forcing it which i wouldn't have time for in the exam anyways. hope you can help Homework Statement...

(1) Is it possible to have a positive acceleration and slow down? (2) Is it possible to have a negative acceleration and speed up? I believe both answers are yes, but I need someone to clarify how. Please help. Thanks

Since the positive reals aren't denumerable (or so do I read) and the positive rationals are, then that must mean the positive irrationals aren't. How do we go on about proving this?

Homework Statement Let n and k be positive integers. Show that k^{1/n} is either a positive integer or an irrational number. The Attempt at a Solution I set q = k^{1/n}. Then I set q = \frac{m}{p} . (Where m and p don't have common factors.) Then m^n = k * p^n . So then k is a factor...

Let n be a positive integer. Define a sequence by setting a_1 = n and, for each k > 1, letting a_k be the unique integer in the range [tex]0 \le a_k \le k-1[/itex] for which \displaystyle a_1 + a_2 + \cdots + a_k is divisible by k. For instance, when n = 9 the obtained sequence is \displaystyle...

Show that \int_0^1 {x^n \sin \left( {\frac{{\pi x}}{2}} \right)} {\kern 1pt} dx > 0 for all {\rm{n}} \ge {\rm{0}} Basically, what i want to show is that over the interval (0,1), the integrand is above the x-axis, or positive. I will show that over the interval, both functions, x^n and...

I solved the following question but I am doubtfull about my results In tug of war,the team that exerts a larger tangential force on the ground wins.Consider the period in which a team is dragging the opposite team by applying larger tangential force on the ground.List which of the following...

I think when we talk about negative or positive of a displacement, we mean that the direction of this displacement which is either going downward or upward. But my question is how about when it says +/-velocity. Does it mean the direction or it means it speeds up or slows down? I think velocity...

Yesterday I asked a question regarding the right hand rule and Lorentz law. I now understand how the right hand rule is applied but the examples I have looked at all involve a positive charge. My question is what effect does a negative charge have on the right hand rule? If for example a...

Since the other thread is closed, I thought I create one with a simple example of water in a tank that most people will understand. Imagine a tank designed to hold water with markers every inch from bottom to top. The marker halfway up the tank is chosen to be labeled zero. The next marker...

2x4 is the same as 4+4 right? they both equal 8 right? by what logic does -2 x -4 = 8. I know its a rule. but why?? shouldn't -4 + -4 = -8 or if it negates itself equal 0? :eek: