Independent Definition and 713 Threads

Homework Statement In the space of 2 by 2 matrices, find a basis for the subspace of matrices whose row sums and column sums are all equal. (Extra credit: Find five linearly independent 3 by 3 matrices with this property) The Attempt at a Solution The first one is ok. The matrix is...

1 Let X be a normal variable with mean 0 and variance 1. Let Y = ZX where Z and X are independent and Pr(Z = +1) = Pr(Z = -1) =1/2. a Show that Y and Z are independent. b Show that Y is also normal with mean 0 and variance 1. c Show that X and Y are uncorrelated but dependent. d Can you...

I was wondering how complex would it be to determine the maxima-minima extrema for a 6 independent variable function? I am assuming it might be enormous if not untenable being that it is all done in "hyper-space" and neither the dependent or all 6 of the independent variables could be visually...

Homework Statement If S = {v1, v2, v3} where v1, v2 and v3 are in \mathbb{R}^2, then the vectors v1, v2 and v3 are linearly independent. Homework Equations NoneThe Attempt at a Solution I thought the answer was true, but I know the correct answer is false and I'm not sure why. Here was my...

simple harmonic motion --> amplitude independent of mass? I know that acceleration is directly proportional to displacement, but opposite in sign, and that acceleration and displacement are related by the square of the frequency. But i was wondering if amplitude is independent of mass in...

Hi, I am confused with respect to these two terms. In a book on regression analysis, I read the following statements. 1. For two normally distributed variables, zero covariance / correlation means independence of the two variables. 2. With the normality assumption, the following...

Homework Statement normalize the wave function \Psi(x)= Acos(\Pi*x/a) to show that A=\sqrt{2/a} The Attempt at a Solution i don't know how to get that answer as all i can tell, normalizing gives: -A^{2}pi^{2}2x/a^{2} * sin (pix/a) However this does not give the right answer for A Any...

There's a PDF attached to this; have I concluded things the right way?

Hi all, I have been studying Linear Algebra for an upcoming exam, and one question has puzzled me slightly! How do you determine of a vector in R4 is linearly independent? Given three vectors, each with 4 rows, I know you are meant to arrange them into a matrix, like this: \[ \left(...

Because according to my book, If A's an invertible nxn matrix, then the eq. Ax=b is consistent for EACH b... this consistency would imply lin. independency?

Homework Statement Suppose that {v1,...,vn} is a linearly independent set in a vector space V and let L:V --> W be a one-to-one linear mapping. Prove that {L(v1),...,L(vn)} is linearly independent. Homework Equations None The Attempt at a Solution If L is a one-to-one linear...

Hi everyone, I've finished the first week of my summer research internship, and I think I desperately need help. I very naively had thought I had "mastered" the art of learning after repeatedly raking in high marks in my courses, but now I feel like I'm completely out of my league and...

Question in the title, ie why is Tr(T_{a_1}T_{a_2}...T_{a_n}) independent of which representation we choose, where the Ts are a matrix representation of the group generators.

[b]1. A fair coin is tossed n times, let E be the event that the first toss is a head and Fk be the event that there are a total of k heads. For which values of n, k are E and fk independent events? [b]3. I don't see how these events can possibly be independent (surely the first influences...

I had an interesting conversation today with one of the senior professors in my department. It was in the context of students who have some difficulty in defining a project. What came into question was the level of independence of Ph.D. students should display with respect to their research...

Hi, I am a little confused how do you find out when a matrix has two independent eigenvectors or when it has one or when it has more than two, or is it possible it can have no eigenvectors.

[b]1. State the one dimensional time - INdependant Schrodinger equation for a particle of mass m and total energy E in a potential V(x). For an infinite square potential well V(x)=0 (0<x<l) and V(x) = infinite (all other x) find a general solutionfor the wavefunction of this function of this...

Hey everyone, I'm working on my undergraduate thesis in biology and am having problems analyzing the data from my experiments. I'm wondering if anyone knows how to compare multiple independent groups when the measurements are proportions. The problem is that many of my values are 1 and 0 with...

So I am going through Serge Lang's Algebra and he left a proof as an exercise, and I simply can't figure it out... I was wondering if someone could point me in the right direction: If f is a polynomial in n-variables over a commutative ring A, then f is homogeneous of degree d if and only if...

Homework Statement Let X and Y be two independent random variables with distribution functions F and G, respectively. Find the distribution functions of max(X,Y) and min(X,Y). Homework Equations The Attempt at a Solution Can someone give me a jumping off point for this problem...

Homework Statement Let the join probability density function of ZX and Y be given by f(x,y)=\left\{\stackrel{2e^{-(x+2y)}\ \ \ \ \ if\ x\ \geq,\ \ \ y\ \geq\ 0}{0\ \ \ \ \ \ \ otherwise} Find E(X^{2}Y) Homework Equations I approached this problem using a theorem from the book that states...

Homework Statement Given: \mathbf{H}=V_0\begin{bmatrix} 1-\epsilon & 0 & 0\\ 0 & 1& \epsilon\\ 0 & \epsilon & 2 \end{bmatrix} \epsilon<<1 a) Find eigenvalues and eigenvectors of the unperturbed Hamiltonian (\epsilon=0) b) Solve for eigenvalues of the Perturbed Hamiltonian...

Hey everyone, I've been thinking about my summer, and I would like to do some sort of research. I applied for some REUs, but it doesn't look like I've gotten into any. However, I would still like to learn something this summer. I've taken DE, Linear Algebra, Abstract Algebra, and...

Assignment question: Let V = P (R) and for j >= 1 define T_j(f(x)) = f^j (x) where f^j(x) is the jth derivative of f(x). Prove that the set {T_1, T_2,..., T_n } is a linearly independent subset of L(V) for any positive integer n. I have no idea how...

Homework Statement Let A = \left[\begin{array}{ccccc} 2&0&-2&1&-3 \\ 1&1&-3&0&-2\\1&0&-1&-1&3 \end{array}\right] a) Find two linearly independent vectors u and v in R5 such that span{u,v}={x \in R^5 : Ax=0}. b) Find three linearly independent vectors u,v and w such that col(A) =...

hi guys, can a time independent system model be controlled via a controller? I am assuming that we can obtain a solution for the model at each sample time, just assume that the model is of c= a*u type, i.e u is input which varing with the time. I am confsed...

Homework Statement determine whether the following are linear independent sets of vectors in the vector space R*R of all functions from R to R a)fn:=1+t+...+t^n for n=1,...4 b) sin,sin^2 ,sin^3 c)1,sin^2,cos^2 Homework Equations The Attempt at a Solution can i do like this for...

There are a wealth of resources... videos, texts, libraries, etc. that are available to us in our studies in physics. Even Physics Forums sections devoted to compiling lists of such resources! For the sake of pacing, discipline, and other reasons (guidance?), who else would be interested in...

I was wondering, if you are told that for two events A and B, We Have P(A)=0.4 and $P(A\mid B) = 0.4$\\ Can you assume as P(A) = P(A\mid B) That these events are independent? regards Brendan

Hi, I'm a bit stuck on this problem A basketball player misses 30% of his free throws. He ends up in a situation where he has the potential to shoot two penalty shots if and only if he lands the first shot (called a one and one, I believe). The outcome of the 2nd shot is independent of the...

Hello all, I am working on this problem, have searched my textbook, this forum, etc and am still as lost. I suspect I need to (in some form) use the formula P(AB)/P(B) = P(A) as it is the integral formula of this section. Any suggestions or hints are greatly appreciated. A fair coin is...

Homework Statement Let u_1...u_n be linearly independent column vectors in R^n and A an invertible n x n matrix. Prove that the vectors Au_1...Au_n are linearly independent. Homework Equations The Attempt at a Solution It is easy to prove this using scalars and the definition of...

Homework Statement When are the vectors (1,x) and (1,y) linearly independent in R^2? When are the vectors (1,x,x^2), (1,y,y^2), and (1,z,z^2) linearly independent? Generalize to R^n. The Attempt at a Solution At first, I think I misconstrued the question and I ended up finding basis...

Homework Statement Let V = {differentiable f:R -> R}, a vector space over R. Take g1,g2,g3 in V where g1(x) = e^{}x, g2(x) = e^{}2x and g3(x) = e^{}3x. Show that g1, g2 and g3 are distinct.Homework Equations If g1-g3 are linearly independent, it means that for any constant, k in F (field) then...

I'm doing a lab where i need to calculate the heat energy, or enthalpy using the equation (delta) H = m x c x T my reactions are going to be of a strong acid and a strong base: Sulfuric Acid + Sodium Hydroxide→ Sodium Sulfate + Water and of a wek acid and the same strong base...

Given random variables X and Y, which are not independent, is it always possible to find a random variable W which is independent from X, such that Y = f(X,W), for some function f? Example: let the joint distribution of X and Y be Y 0 1 X+------- 0|1/3 1/6 1|1/6 1/3 Then if we...

I have 1000 experiments on the same data, each of which is trying to decide the probability that the data agrees with a model. The problem is, even if each experiment REALLY agrees with the model (ie. p(d1) = .99, p(d2) = .99, etc), when I multiply these together to get P(d1 & d2 & d3... &...

Einstein wrote ... Q: What would happen inre (in regards to) time if, for any reason, a clock were to be 'independent of the state of motion of [its] body of reference'? A: _____ (?)

Homework Statement Given vectors: a1 = (1; 2; 0), a2 = (2; 1; 3), a3 = (0; 3; -3). Find out if these vectors are linearly independent. Homework Equations The Attempt at a Solution \begin{cases}...

If you have a 3x3 matrix AB of rank 2, and you are asked to find two linearly independent vectors in the column space of A, are those the same vectors in the column space of AB? I figure it is since if the vectors are linearly independent they wouldn't change. Am I right?

Can two independent sources of light be coherent?

Hi guys, I am solving a problem in the form: (ATx=0 where A is a matrix of known numbers and I am solving for x. After performing reduction and multiplying ATx, I am left with the following equations: -X1 + X4 - X5 = 0 -X2 + X4 = 0 -X3 + X4 -X5 + 28X6 = 0 From these equations, I...

What kind of knowledge do independent invent0rs have? Do they have knowledge in all the areas of engineering? Thanks!

I'm looking to do a guided independent study course at my college next term; the college doesn't offer physics beyond the introductory calculus-based sequence, which I've completed, and I'm not yet ready to transfer. The physics major sequence at the school to which I intend to transfer...

Hi everyone, I know this subject has been broached before but would appreciate some extra help - I'm an English major in second year uni so I haven't done physics and maths for a while, but I have quite a lot of free time at the moment and would really love to get back into these subjects...

Homework Statement If the current density is time independent and divergence free, show that the Maxwell Equations separate into independent equations for \vec{E} and \vec{B}. Homework Equations Maxwell's equations The Attempt at a Solution The only Maxwell equation with \vec{j}...

So the question is... Let v1, v2,...,,vn be linearly independent vectors in a vector space V. Show that v2,...,vn cannot span V. I honestly have found myself completely lost lately and I suck at writing proofs. So this is what I see, v1, v2,..., vn is linearly independent iff...

I would appreciate some help with this problem. Assuming X and Y are independent, I'm trying to find the correlation between XY and Y in terms of the means and standard deviations of X and Y. I'm not sure how to simplify cov(XY,Y)=E(XYY)-E(XY)E(Y) =E(XY^2)-E(X)E(Y)^2. If X and Y are...

\varepsilon _t = z_t \sigma _t z_t \sim IID\,N\left( {0,1} \right) \sigma _t^2 = f\left( {\sigma _{t - 1} ,z_{t - 1} } \right) Are the epsilons independent from each other? Why?

If nuclear forces would be spin independent! HI all,a question was asked by my teacher that "if nuclear forces would be spin independent then how many types of DEUTRON would be existing and what would be their relative abundances. Please help Thanks