Independent Definition and 745 Threads

Suppose we had an infinite series - z = ∑i = 1 to ∞ ( α1(i)x1 + α2(i)x2 + . . . + αm(i)xm ) - rewritten as the cumulative sequence - z(n) = α1(n)x1 + α2(n)x2 + . . . + αm(n)xm - where the xj are linearly independent and normalized (and serve as a finite basis across the sequence). If all...

Ok for starters, I am sorry for the length of the question and jamming multiple questions in here i feel like my doubts are all related and it would be best just to put it all in one place instead of creating 2-4 topics. I'm beginning to feel confused with the amount of ways i see people...

okay so i need some help interpreting some of the results, so (-ħ2/2m)Ψ''=E-V0Ψ; So i set k2= 2m*(E-V0)/ħ2 and so : Ψ''=-k2Ψ so if V0=0 or is smaller than E, k2 is positive; *need for help starts here* Ψ=Aeikx+Be-ikx; another result for this would also be only eikx so is the second term only...

Functions are pretty simple things , they just express a relationship between two different quantities How do i express this function in terms of y(x) = something ?

Homework Statement Two flies were crossed one wildtype another double mutant sepia(se) and vestigial(vg) yielding 40% wild type 40% se vg, 10% se and 10% vg. The genes show- a.Complete linkage b.Incomplete linkage c.Independent assortment d. epistasis 2. The attempt at a solution Since no. of...

These are two example where it seems they are both independent but the second one is not. Why? First problem. There are 100 balls numbered 1 through 100 in a bag and one ball is randomly picked and returned to the bag for the next pick. There is event A that the ball picked is divisible...

Homework Statement [/B] https://www.physicsforums.com/attachments/screen-shot-2017-04-15-at-12-28-52-pm-png.194886/?temp_hash=4939cc24bd25e6adfbe75458bec6d011 Homework Equations [/B] P(X∈A,Y∈B)=P(X∈A)×P(Y∈B) The Attempt at a Solution If X and Y are independent then: P(X∈A,Y∈B)=P(X∈A)×P(Y∈B)...

How does lemma 18.2.2 imply the definition?

Hey y'all, my first thread here, Got a burning question that has been disturbing my serenity. In all derivations of the stress tensor that I've seen they didn't explain it that much, So my question is, why do the traction vectors on each surface are independent? From what I understood, the...

Homework Statement Let ##T## be a linear operator on a vector space ##V##, and let ##\lambda_1,\lambda_2, \dots, \lambda_n## be distinct eigenvalues of ##T##. If ##v_1, v_2, \dots , v_n## are eigenvectors of ##T## such that ##\lambda_i## corresponds to ##v_i \ (1 \le i \le k)##, then ##\{ v_1...

I've thought of a new way (at least I never read it anywhere) of counting the independent components of the Riemann tensor, but I am not sure whether my arguments are valid, so I would like to ask whether my argument is sound or total bonkers. The Riemann tensor gives the deviation of a vector A...

I am interested in pursuing a masters in electrical engineering at a non-top tier university (UTD). As I understand it, the masters thesis option at most universities is the main priority, as they are job openings that need to be filled. Then the masters non-thesis students are used to fill in...

A rocket is drifting in gravity-free space and is observed by an external observer who is also drifting at an unchanging location using an arbitrary coordinate system. The rocket accelerates at a fixed rate using a massless photon engine that results in a negligible change in the mass of the...

Hello, Just wondering if the trace of a matrix is independent of basis, seeing as the trace of a matrix is equal to the sun of the eigenvalues of the operator that the matrix is a representation of. Thank you

Homework Statement My lecture note says that "T-v diagram shows change in specific volume of a substance with respect to temperature.". Is it correct? Homework EquationsThe Attempt at a Solution If a(Specific Volume) "with respect" to b(Temperature), then b(Temperature) should be the...

Homework Statement You have a circuit supplied with AC voltage, it has 2 parallel branches, 1 with R and L, the other with R and C. a) If (frequency) w^2 = 1/LC, prove that the power in each branch is equal. b) If R^2 = L/C, show that the power is the circuit is independent of frequency...

Hi. I'm a bit puzzled that the classical formula for the intensity of a monochromatic, linear EM wave $$I=\frac{1}{2}\cdot c\cdot \varepsilon_0\cdot E_0 ^2$$ seems to be independent of frequency whereas I find for the energy of a mechanical wave (e.g. on a string with total mass ##M##)...

Homework Statement Given the bessel equation $$x^2\frac{d^2y}{dx^2} + x\frac{dy}{dx} -(1-x)y=0$$ show that when changing the variable to ##u = 2\sqrt{x}## the equation becomes $$u^2\frac{d^2y}{du^2}+u\frac{dy}{du}+(u^2-4)y = 0$$ Homework Equations The Attempt at a Solution ##u=2\sqrt{x}##...

Homework Statement If ##r_1, r_2, r_3## are distinct real numbers, show that ##e^{r_1t}, e^{r_2t}, e^{r_3t}## are linearly independent. Homework EquationsThe Attempt at a Solution By book starts off by assuming that the functions are linearly dependent, towards contradiction. So ##c_1e^{r_1t}...

So, I talked to my professor about doing research and he said that I can start next semester either with his group which is working on supernova or I can find my own topic and work independently (or do both). I have decided to work with his group just because I really like the research topic and...

Let ##f(x,y,z)=x^2e^{-x-xy-xz}##, if ##x,y,z>0## and ##f(x,y,z)=0## otherwise. Are the continuous random variables ##x,y,z## independent or not? Intuitively they are not independent. I calculated the marginal density functions: ##f_x(x)=\iint_{\Omega} f(x,y,z) dydz=e^{-x}##...

Homework Statement Homework Equations The Attempt at a Solution I set up the Wronskian?? and compare them?

I know that D is definitely a dependent variable, but I don't see how the others are dependent on anything else... The correct answer is A btw. Please explain to me how B and C are dependent variables considering the investigation is to "determine and compare the heat of combustion of three...

how can you say(prove) that Newton's third law is frame independent. you will say that as real forces are frame independent , therefore Newton's third law is also frame independent, so tell me how real forces are frame independent?

If equation of motion(K-G Eqn.,) follows, ∂μ∂μΦ+m2Φ=ρ where 'ρ' is point source at origin. How time independent form of above will become, (∇2-m2)Φ(x)=gδ3(x) where g is the coupling constant, δ3(x) is three dimensional dirac delta function.

Homework Statement (b) (10 points) Estimate the equation income = β0 + β1female. Interpret theβ1 coefficient. How does β1 compare to your difference in means in part a? (c) (10 points) Estimate income as a linear function of highest grade and female. Report results. How does the coefficient on...

Hi PF! The other day in class my professor mentioned something about expanding linear independent vectors, but he did not elaborate. From what I understand, if ##x_1,...,x_k## are linearly independent vectors in ##V##, where ##dimV=n>k##, how would you extend ##x_1,...x_k## to a basis ##\{...

Why do we take a particle's position ##x## and its velocity ##\dot{x}## as independent variables in a phase space when they are dependent in the sense that given the function ##x(t)##, we can get the function ##\dot{x}(t)##? I'm thinking they are independent variables but not independent...

Homework Statement Lets say f(x) is a solution to TISE. If it is, why is its complex conjugate f*(x) a solution too? Homework Equations TISE = time independent Schrodinger equation The Attempt at a Solution ?

(sorry for the horrible butchered thread title... should say "determination", not "determining") 1. Homework Statement In "Principles of Quantum Mechanics", by R. Shankar, a vector space is defined as having dimension n if it can accommodate a maximum of n linearly independent vectors (here is...

Hello all, Suppose I have the following summation ##X=\sum_{k=1}^KX_k## where the ##\{X_k\}## are independent and identically distributed random variables with CDF and PDF of ##F_{X_k}(x)## and ##f_{X_k}(x)##, respectively. How can I find the CDF of ##X##? Thanks in advance

Hi everyone, i'm not able to find the exact definition of mass independent renormalization scheme. I often read that the MS-bar scheme is mass independent, but why? And why this feature help us to compute the beta function? Thanks in advance, Luca

Hello, I just completed a first course in linear algebra and really enjoyed my studies. So much so that I want to pursue it more in the fall as an independent study, i am a EE major in college and was curious what directions might be useful for applications in that field.

Is it possible to combine (possibly infinite) capacitors and inductors to get a total impedance which is independent of frequency. If so, how?

mentor note: moved from General Math to here hence no template (OP is not a student) Hello, Need some math help on a problem I am facing. I need to take 2 resultant values and frame them within a range of 0 to 100. Values - t, x f(y) = t/x where t= time, x = power I need to have the...

Is the "gradient" vector a concept that that is coordinate independent ? For example, the concept of a vector representing a force is independent of what coordinate system is used to represent the vector. So is a "gradient vector" such a physical vector ? The web page...

What 20 index combinations yield Riemann tensor components (that are not identically zero) from which the rest of the tensor components can be determined?

How can I find out if this matrix A's columns are linearly independent? $\begin{bmatrix}1&0\\0&0\end{bmatrix}$ I see here that $x_1 = 0$ and similarly $x_2 = 0$ does this mean that this matrix A's columns are therefore linearly dependent? Also this is a projection onto the $x_1$ axis so is it...

Hi everyone I have a quick question about independent and dependent variables. Homework Statement The following data set gives the number of miles traveled, and the travel time in hours for each of the 10 car's driving assignments. Miles Time 90 9 40 5 90 9 90...

Is the rate of radioactive decay fixed or does the environment have any impact eg would the rate of decay be the same in a low or very high gravitational field (in both cases measured from the viewpoint of the radioactive material)?

Is latex balloon maximum strain independent of latex thickness? I have been in search of a latex balloon that is relatively small when deflated and very large when fully inflated. Standard balloons that reach the desired inflated dimensions are much larger deflated than I would like...

If we use n linearly independent vectors x1,x2...xn to form a vector space V and use another set of n linearly independent vectors y1,y2...yn to form a vector space S, is it necessary that V and S are the same? Why? If we have a vector space Q that the dimension is n, can we say that any set of...

Homework Statement Let(v1, v2, v3) be three linearly independent vectors in a vector space V. Is the set {v1-v2, v2-v3, v3-v1} linearly dependent or independent? Homework Equations Linearly independent is when c1v1+c2v2+...+ckvk=0 and c1=c2=...ck=0 The Attempt at a Solution c1(v1-v2)+...

I have been asked by someone if it is true that in general, for a constantly accelerating reference frame, i.e. a non-inertial reference frame, the acceleration of a particle (as observed in this frame) due to the corresponding fictitious force is independent of its mass. My response was yes...

Why absolute zero of temperature doesn't depend upon properties of substance?

I want to know why is the measurement of acceleration independent of inertial reference frames? I mean if displacement, velocity varies with change of inertial reference frames, acceleration should vary. And, one more question: When we say that displacement or velocity varies with change in...

If young modulus = stress/strain Wouldn't a different original length affect the value of young modulus ?

Hi everybody, I'm a second semester physics major who was fortunate enough to get a position in a research group at my school. What I want to do is get a head start on learning the physics that this lab studies. Currently, I'm in the honors section of basic E & M and I do well in class, not...

Is there any way to design a lens or system of lenses where I see the same part of the image, irrespective of direction or angle of view. The light rays can be assumed to be collimated as viewing will be from a distance. Actually- I am looking at focusing on a point or specific area of the...

"Is it possible to create an independent Venus aerostats?" Introduction to Venus. Almost everybody here knows the planet Venus. Our bright sister planet, and the hell of all. But at the altitude of about 53 km, conditions here is so far the most Earth-like in the solar system, with near-Earth...