Independent Definition and 713 Threads

Homework Statement True or false. If v1... v4 are linearly independent vectors in 4D space, then {v1,v2,v3} is also linearly independent. There's a hint: Think about (c for different constant) cv1+cv2+cv3+0*v4=0 I know that linear independence means there's only the trivial solution... which...

In my course notes for atomic physics, looking at time independent perturbation for the non-degenerate case, we have the following: http://i.imgur.com/ao4ughk.png However I am confused about the equation 5.1.6. We know that < phi n | phi m > = 0 for n =/= m, so shouldn't this mean that < phi n...

Homework Statement Definition of spanning set: Let be vectors in the vector space . The set of all linear combination of the vectors is a subspace ( say ) of . The subspace is called the space spanned by the vectors The set is called a spanning set of . Definition of linear independence...

Well folks, I am a bit confused with this apparently "simple" system of equations. pa=Probability player A wins a point when he is on serve qa=1-pa=Probability player A loses a point when he is on serve pb, and qb are the same for player B when he is on his own serve I have calculated the...

Hello everyone How is it possible that a n-dimensional spacetime admits m> n INDEPENDENT Killing vectors where m=n(n+1)/2 if the space is maximally symmetric?

Hey all, student100's brother here, he got me to create an account to ask my question here... I'm taking an introduction to linear algebra class and we had a test problem to prove a set of vectors is linear independent: ##V = v_1, \dots, v_n \in \Bbb R^n## such that each element of the set is...

Good morning everyone! My chemistry final is approaching and I have a few difficulties in the thermodynamics chapter. One of the things that are bothering me is the calculation of the temperature of phase change. We know that if a mole of ice at 273K melts, the entropy change would be...

Why is rotational equilibrium condition independent of origin about which torques are taken?

In a source-free, isotropic, linear medium, Maxwell's equations can be rewritten as follows: \nabla \cdot \mathbf{E} = 0 \nabla \cdot \mathbf{H} = 0 \nabla \times \mathbf{E} = -j \omega \mu \mathbf{H} \nabla \times \mathbf{E} = j \omega \epsilon \mathbf{E} If we are looking for a wave...

Homework Statement Verify that a plane wave ψ(x) = Ae-ikx is a solution to the time independent Schrodinger equation for a free particle in one dimension. Can it be normalised? Why?[/B]Homework EquationsThe Attempt at a Solution My lecturer's notes are all over the place, which is frustrating...

Homework Statement Recently, I have been wondering whether forces are independent of reference frames(inertial and non inertial). From Newton's law we know that the second law is valid only for inertial frames. But what about the non inertial frames. Let ∑F be the net force on an object in an...

Homework Statement Given X,Y,Z are 3 N(1,1) random variables, (1) Find E[ XY | Y + Z = 1] Homework EquationsThe Attempt at a Solution I'm honestly completely lost in statistics... I didn't quite grasp the intuitive aspect of expectation because my professor lives in the numbers side and...

Hi all, Due to a scheduling conflict at my university I can't take Discrete Math, and it's a pre-requisite for all of the math courses I want to take next year. Any recommendations on which textbooks I ought to use to independently study the subject? Thanks!

Are the four classes of quantum mechanical phenomena for which classical physics cannot account independent of one another or can one derive one or more phenomena from other(s)? These according to the Wiki are: Principle of uncertainty; Wave-particle duality; Quantisation of certain physical...

A manufacturer has designed a process to produce pipes that are 10 feet long. The distribution of the pipe length, however, is actually Uniform on the interval 10 feet to 10.57 feet. Assume that the lengths of individual pipes produced by the process are independent. Let X and Y represent the...

It's non-trivial since if you do not have a background metric you cannot define the scale, with respect to which couplings are supposed to run. So new approaches to renormalization have appeared. Perimeter has a workshop on this and a number of Monday 28 Sep talks are on line...

Homework Statement Two cards are drawn in succession without replacement from a standard deck. Show that the events A = ”face card on first draw” and B = ”heart on second draw” are independent. Hint: Write A = A1 ∪ A2, where A1 = ”face card and a heart on first draw” and A2 = ”face card and...

Homework Statement Prove that a set of linearly independent vectors in Rn can have maximum n elements. So how would you prove that the maximum number of independent vectors in Rn is n?I can understand why in my head but not sure how to give a mathematical proof. I understand it in terms of the...

Hello, I'd like someone to double check my maths please, it wasn't the greatest at school and that was a few years ago! If I am incorrect could you please tell me the correct answer as well as show me how to apply it so I can figure out similar problems myself. Thanks. Yes, this is about...

Hi, hopefully some of you on this forum get where I am coming from and can help with this. For the people here working outside of academic institutions or money paying jobs, people who do proper academic-level science off there own back...how do you find satisfaction with it? Feel like you...

Hi, I was woking on a problem from Taylor Mechanics.(4.27) It reads: Suppose that the force F(r , t) depends on the time t but stillsatisfies ∇ × F = 0. It is a mathematical fact that the work integral ∫12F(r , t) ⋅ dr (evaluated at anyone time t) is independent of the path taken between the...

http://www.sciencedirect.com/science/article/pii/S0273117715005712 from the abstract: Obviously, the most prominent missing 'forcing' parameter here, is "concentration of greenhouse gasses". There is probably some food for thoughts here, especially when the analysis of Den Volokin and Lark...

How can I convert this system of equations : $$\frac{dz}{d\phi} = \frac{rB_z}{B_{\phi}}, \frac{dr}{d\phi} = \frac{rB_r}{B_{\phi}}, \frac{d\phi}{d\phi} = 1$$ to $$\frac{dr}{dz}, \frac{d\phi}{dz}, \frac{dz}{dz}$$

let A B B' be Bell usual matrices for spin 1/2. Are the results of $$A\otimes B$$ and $$A\otimes B'$$ independent ? I cannot imagine the contrary since on what could they depend all angles are fixed.

Hey all. I am currently reading an article and there is a paragraph that I am having a hard time understand. This is what the paragraph says: "Since Ar = Arτ and Ai = -Aiτ, we know that only the lower triangular (including the diagonal) elements of Ar are independent and only the strictly lower...

I have it on good authority that decoherence (probably) solves the preferred basis problem and explains the suppression of interference phenomena; however there remains the question: why do we get outcomes at all? Unitary evolution of coupled systems results in entanglement and thus an improper...

I'm just learning about the whole Dirac notation stuff and I have come across the fact that bra's and ket's are somehow independent of bases. Or rather that they do not need the specification of a basis. I really don't understand this from a vector point of view. Maybe that is the problem...

Homework Statement Consider a one-dimensional, nonrelativistic particle of mass m which can move in the three regions defined by points A, B, C, and D. The potential from A to B is zero; the potential from B to C is (10/m)(h/ΔL)2; and the potential from C to D is (1/10m)(h/ΔL)2. The distance...

Hello, I'm trying to reconcile what seems to me to be a contradiction. Last week, I did a lab experiment where we stacked some metal bars in a tray and measured the force required to pull the tray into motion and break away from the force of static friction. As we predicted, the more mass we...

What are the basics of non commutative geometry and where is a good place to learn more about it?

Hello! (Wave) An independent set of a graph $G=(V,E)$ is a subset $V' \subseteq V$ of vertices such that each edge in $E$ is incident on at most one vertex in $V'$. The independent-set problem is to find a maximum-size independent set in $G$. Formulate a related decision problem for the...

PF Family, I love my undergraduate institution. However, our physics department is very small and has a very small faculty. Also, although many are listed on the webpage, we only have one physics elective, "Intro to Astronomy", which I am not very interested in. I've been thinking about...

In calculus of variations when we solve Euler's equation we always do think of y, x and y' as independent variables. In thermodynamics we think that different potentials have totally different variables I don't understand why the slope of the function is not directly dependent on function itself.

Hi all, I am in 7th grade science, but I have a lot of interest in advanced physics (and I am really bored in class), so I am currently working on an independent project on field theory (both classical and quantum). I understand it well, although my background in calculus is not great (I have...

I am really not sure about this ... I may be generalizing it ...but anyway... suppose we have two resistors in series...connected by ofcourse a voltage source...and a certain amount of total current is flowing through the whole circuit.. now if we want to make the total current totally...

In the photoelectric effect, we observe that the stopping potential is independent of the intensity of the light. This is readily explained by the photon hypothesis. One often sees the statement that in "the classical theory," the stopping potential should increase with intensity. What...

Homework Statement Homework Equations The Attempt at a Solution a) For this part, I know for distinguishable particles, the expectation value of the square distance $$\langle (x_{1}^{2} - x_{2}^{2}) \rangle = \langle x^{2} \rangle_{2} + \langle x^{2} \rangle_{3} - 2 \langle x \rangle_{2}...

Homework Statement Is the gaussian $$\sqrt{\frac{\pi}{2\alpha}}e^{-\alpha x^{2}}$$ an eigenfunction of ## \widehat{T} = \frac{\hat{p}^{2}}{2m}## ? If so, what is the corresponding eigenvalue? If not, find a P.E. operator ##\widehat{U} = U(\hat{x}) ## which gives rise to a Hamiltonian...

There are two categories of objects, A and B. From long term observation, experiment 1 is known to be 70% accurate i.e. it predicts type A or B correctly in 70% of cases. Experiment 2 is totally independent. It uses different methods and different characteristics. It is also known to predict...

Homework Statement A linear transformation with Matrix A = ## \begin{pmatrix} 5&4&2\\ 4&5&2\\ 2&2&2 \end{pmatrix} ## has eigenvalues 1 and 10. Find two linearly independent eigenvectors corresponding to the eigenvalue 1. Homework Equations 3. The Attempt at a Solution [/B] I know from the...

Homework Statement Solve 2x''+3x'+40x = 40y+3y' Homework Equations y = 0.05sin(10t) The Attempt at a Solution I used the annihilator method to find the answer of x(t) = Acos(10t)+Bsin(10t)+Ce-0.75tcos(sqrt(311)/4t)+De-0.75tsin(sqrt(311)/4t) where A, B, C and D are constants. The initial...

Hey guys, I'm an undergrad looking to do hep-th / mathematical physics in grad school, and have a free summer to kill. I have two options: a) Independent studies in QFT and GR. b) Research in hep-ph that won't be very mathematical, but will probably lead to a paper. If you were in my position...

For a mass-spring system, Period, T = 2pi * root(m/k) So using hookes law, F = kx But if the spring is being stretched by a mass due to gravity, mg = kx So, k = mg/x But then this means, Period, T = 2pi * root(mx / mg) or, T = 2pi * root(x / g) Where have I gone wrong? I've been told...

Is it possible that the potential energy depends on the time and the system is conservative? Let me elaborate. Consider a function ##U(\vec{r},t)## and consider the case where the forces in space at any moment are given by ##\vec{F}=-\nabla{U}##. So in this case, according to the definition of...

I'm talking about this: http://www.cs.cornell.edu/courses/cs6650/2008fa/images/thumb_EL.jpg In the derivation when you minimize action you assume that all the variations in coordinates are independent and thus conclude that each term has to be zero. When this isn't the case anymore one doesn't...

Consider a simple textbook problem in two dimensional kinematics - say, a projectile motion problem. I know that the x- and y- components of motion are independent of one another but I don't understand why. I know this is true due to everyday observation - empirical evidence of this being the...

I have a load cell which must be placed onto a piece of vehicle structure. In an ideal world I would attach the load cell to the structure and calibrate both together to ensure a very accurate calibration, and that accurate loads are measured. However a problem arises if I need to replace the...

Homework Statement Consider three events A1, A2, and A3, and let pi = P(Ai), for i = 1, 2, 3. a) Express the probability that at least one of these three events occurs in terms of the pi ’s. b) Express the probability that at least two of the events occur. c) Suppose that A1, A2 and A3 are...

Hello, the TISE can be simplified $$H \psi = E \psi$$ Where ##H## is the Hamiltonian, and ##E## is the eigenvalue, but why don't the ##\psi## terms cancel, leaving ##H = E##? Also, what the heck does the eigenvalue ##E## have to do with the eigenvalue that I have previously encountered in...

Let's say we've a system which can be described by the Hamiltonian: $$H_0 = \dfrac{p^2}{2m} + V(x)$$ Now suppose we introduce a perturbation given by: $$H_1 = \lambda x^2$$ Our total hamiltonian: $$H = H_0 + H_1 = \dfrac{p^2}{2m} + V(x) + \lambda x^2 $$ Normally, the perturbation doesn't...