Geometric Definition and 813 Threads

Homework Statement I'm not interested in the proof of this statement, just its geometric meaning (if it has one): Suppose T \in L(V) is self-adjoint, \lambda \in F, and \epsilon > 0. If there exists v \in V such that ||v|| = 1 and || Tv - \lambda v || < \epsilon, then T has an...

Hi, I have a problem with computing this geometric series. Homework Statement I have to compute \sum_{i=0}^\infty{(\frac{1}{2z})^{2k}} + \sum_{i=0}^\infty{(\frac{1}{3z})^{2k+1}}. It's for computing the z-transform of f[k]=0 for k<0 f[k]=(\frac{1}{2})^k for k=0,2,4,6...

Homework Statement Homework Equations The Attempt at a Solution I don't get what I am doing wrong here, I have attached my solution below. The solution manual have their answer as 3e/(3-e). Thanks!

Homework Statement a) Two friends, Jon and Bob, are sharing a loaf of bread. Jon eats half of the loaf, then Bob eats half of what remains, then Jon eats half of what remains and so on. How much of the loaf did each of them eat? b)Jon is hungrier and eats 2/3 of the loaf, then Bob eats half...

helo this is a homework problem i got in math 30 pure i got an answer but i would like to know how to get it by using a formula? The exercise gose like this: Initially, a pendulum swings through an arc of 2feet. On each successive swing,the length of the arc is 0.9 of the previous length...

I getting far enough into my geometric algebra books now that I'm at linear transformations, including the result showing how a linear transformation inverse can be expressed directly as a geometric product, using the adjoint and pseudoscalar multiplication, instead of using matrix inversion...

Hi In trying to calculate the following sum: \sum_{i=1}^n{i^2} I found the following expansions: \sum_{i=1}^p \sum_{j=0}^{i-1} (-1)^j(i-j)^p {n+p-i+1\choose n-i} {p+1\choose j} My question is: is there an easier or more intuitive way to compute the limit of the sum above?

My differential forms book (Flanders/Dover) defines an inner product on wedge products for vectors that have a defined inner product, and uses that to define the hodge dual. That wedge inner product definition was a determinant of inner products. I don't actually have that book on me right...

I was given an ap problem in class, specifically: Problem 2:http://www.collegeboard.com/prod_downloads/ap/students/calculus/b_calculus_bc_frq_03.pdf I was able to do it just fine, but then I had the idea to try and solve it geometrically/algebraically. However, I haven't been able to come...

Stats -- Geometric Variance Proof Hi, I'm a student in South-East Indiana, enrolled in a AP Stats class. Our teacher has asked us to prove the geometric variance equation (the first equation pictured) USING ALGEBRA ONLY. I've gotten it all the way down to the 2nd equation and now I'm stuck...

Given the parametric representation of two planes, through points P and Q respectively x = P + \alpha u + \beta v y = Q + a w + b z Or, alternately, with u \wedge v = A, and w \wedge z = B x \wedge A = P \wedge A y \wedge B = Q \wedge B It's easy enough to find...

Hi all, We are now going to do a kind of experiment in which we use a plumb bob to identify the vertical direction. But I think, the pumb string will point to the center of mass, while we need the geometric center . I mean the COM of the Earth is diffent from the geometric center and it...

geometric algebra cross product -------------------------------------------------------------------------------- Homework Statement [/b] my text (Geometric Algebra for Physicists, by Doran and Lasenby), p. 69, deals with rotating frame {fsubk} (I assume in 3D) d/dt (fsubk) = omega X...

Homework Statement [/b] my text (Geometric Algebra for Physicists, by Doran and Lasenby), p. 69, deals with rotating frame {fsubk} (I assume in 3D) d/dt (fsubk) = omega X fsubk omega being angular velocity then omega X fsubk = (-I omega) dot fsubk = fsubk dot (I omega), where...

Does anyone know how to evaluate S_n = \sum_{i=0}^{n-1} i2^i I tried the following. Let r = 2, and figure out the terms in S_n - rS_n Unlike with a regular geometric series, this does not make all but two of the terms disappear. But it does make all but one of the terms turn into a...

Homework Statement A river is 2 km wide and flows at 6 km/h. A motor boat that has a speed of 20 km/h in still water heads out from one bank perpendicular to the current. A marina lies directly across the river on the opposite bank. Use Geometric Vectors to solve this problem. a. How far...

[SOLVED] Geometric Vectors Homework Statement Find the magnitude and the direction (to the nearest degree) of the resultant of each of the following systems of forces. a. forces of 3 N and 8 N acting at an angle of 60º to each other - use geometric vectors to solve this problem...

Let A and B be similar matrices. Prove that the geometric multiplicities of the eigenvalues of A and B are the same. Some help I have gotten so far but still don't know how to proceed from there: To prove that the geometric multiplicities of the eigenvalues of A and B are the same, we can...

Homework Statement Determine the sum of the series: \sum^{infinity}_{K=10} \frac{7}{e^(3k+2)} Homework Equations The Attempt at a Solutionlimit n->infinity of sn=\sum^{n}_{K=10} \frac{7}{e^(3k+2)}=\frac{7}{e^(32)}+\frac{7}{e^(35)}...\frac{7}{e^(3n+2)} This series does not exactly fit a...

Homework Statement See images. . . Can you please correct my answers if I get some of them wrong? Homework Equations There aren't really any relevant equations to solve the problemsThe Attempt at a Solution See images. . .

I am trying to teach myself and often get stuck. Right now I've come across a . B = 1/2(aB-Ba) where a is a vector and B is a bivector. what's confusing me is that it seems to require a change in the definition of geometric product as the sum of a symmetrical inner product and...

Homework Statement Consider the following infinite geometric series: 1 + (2x/3) + (2x/3)^2 + (2x/3)^3 + ... for what values of x does the series converge? Homework Equations i don't know what converge means, i guessed it was for what vlaues does the geometric series is infinite but...

Homework Statement How can I simplify sum from j=0 to infinite of x^(2j) ? Homework Equations The Attempt at a Solution THis is close to the geometric series but I'd have to square each individual term

Homework Statement Describe geometrically the sets of points determined by the relations: a) |z-i|+|z-1| = 2 b) |z-i|=|z+1| c) Re z = |z-2| Homework Equations The Attempt at a Solution I know the answer of a is suppose to be Ellipse with foci at i and 1, major axis 2 and b...

Homework Statement Which of following sets of conditions (A - F), if true, would show that the expressions 1 and 2 above define the same vector C_vec as expressions 3 and 4? 1. The two pairs of expressions give the same length and direction for C_vec. 2. The two pairs of...

i was doing some exercises nut I'm not sure if my answers are correct 1) X~B(5,0.25) i have to find: a) E(x^2) and my answer was 2.5, is this correct? b) P(x(>or=to)4) and my answer was 0.0889, is this correct? 2) X~Geom(1/3) i have to find: a) E(x) my answer is 1/3 b) E(x^2) c)...

Homework Statement 3. The following calculaltion shows how the ratio of e to kT affects the populations of different energy levels. kT is sometimes called the thermal energy; if it is small relative to e, a particle will not be able to access higher energy states. Consider a harmonic...

Homework Statement The common ratio,ratio,r, of a geometric series is given by: r=\frac{5x}{4+x^2} Find all the values of x for which the series converges Homework Equations The Attempt at a Solution For the series to converge |r|<1 so that |\frac{5x}{4+x^2}|<1 this...

Geometric Models: E8, SO(10), Which ansatzs will prove to be right by CERN? 1. Ali H. Chamseddine and Alain Connes , SO(10) …. the spectral action associated with this noncommutative space unifies gravitation with the Standard Model at the unification scale. … Therefore the bare action we...

Homework Statement I am trying to see the geometric interpretation of the generalized MVT. It is not a homework problem, but would like to know how to interpret the equation Homework Equations [f(b)- f(a)]* g'(x) = [g(b)- g(a)]* f'(x) The Attempt at a Solution On...

I'm currently putting together a basic summary of the Lambda-CDM model and I have a slight issue with the fact that the equation to calculate lambda (which includes factors to convert physical units into geometric units) is incorporated into the omega_lambda calculation (which incorporates the...

Hi everyone! So I'm trying to learn more about inequalities and the one I'm starting with is the power means inequality. But it all seems pretty intuitive except how they define the n=0 power mean (i.e. the geometric mean). I read that it's actually the limit as n->0, but I don't see why that's...

T is the projection onto the xy-coordinate plane: T(x,y,z)=(x,y,0) I have to give a geometric description of the kernel and range of T. my geometric description of the kernel: a line along the z-axis. Is this correct? whats the geometric description of the range of T?

let T:R^{3} \rightarrow R^{3} be a linear transformation. how can i figure out a geometric description of the kernel and range of T. What do I have to look at?

Homework Statement You work for MOONOCO, an oil company that has a drilling platform one mile due north of a long straight shoreline that goes east and west. MOONOCO has three storage depots on land. The first (Depot Alpha) is on the shoreline four miles west of the nearest point on shore to...

Homework Statement Use cos ( n * x) = (z ^ n + z ^ -n)/2 to express cos x + cos 3x + cos 5x + ... + cos([2n -1]x) as a geometric series in terms of z. Hence find this sum in terms of x Homework Equations The Attempt at a Solution (z + z^-1)/2 + (z^3 + z^-3)/2 + ... +...

I've been studying absolute uncertainties and do not understand any of it. If someone can explain it will really help. Especially with uncertainties including diameters and area.

Homework Statement Give a geometric description of the Span {V_{1},V_{2}} for the vectors V_{1} = [8, 2, -6] and V_{2} = [12, 3, -9] Those should be columns but I couldn't figure that out in latex, sorry. 2. The attempt at a solution I have a solution, what I need help with is...

hi this is my first participation in this forum I want aske some quastions what is the paraquantization ? can we devloppe a geometric paraquantization? how can demonstrate that the green anzats is equivalent to tri commutation relation of parastatistical particle

I'm sure many of you guys have seen the videos of a beam of light (namely a laser of some sort) pass through a volume of liquid in which there is a gradient of index of refraction from the bottom of the tank to the top. Think of a sugar solution in which more sugar collects at the bottom and...

Hello all. I wasd beginning to feel at home with vectors and covectors but while trying to fully understand the concepts this query came up._________ Excuse the lack of rigorous definition but I think you will realize what I am aiming at. Take a geometrical vector in a finite...

is it possible to have an virtual OBJECT in image formation?

Homework Statement Let A be an arbitrary vector and e be a unit vector in some fixed direction.Show that A=e(A.e)+e x (A x e) What is the geometrical significance of each of the two terms? Homework Equations The Attempt at a Solution I can show it easily.As the first term (a dot...

For the molecule \textrm{Ni}\left(\textrm{OH}\right)_{2}\textrm{Cl}\left(\textrm{NH}_{3}\right)_{3}, how do you determine the number of geometric and optical isomers? I first drew the molecule with a central \textrm{Cl} bonded to three \textrm{NH}_{3} molecules and a \textrm{Ni}; the...

I tried to obtain refraction of light by sun's gravity by substitution of sun's gravitational field by aether with different speeds of light. I do not get right result. Where I am wrong? For light which travel close to the sun by direct trajectory, I get the following speed of light in...

Homework Statement (infinity)sigma(k = 0) [2(2/6)^k + (-2/10)^k) Homework Equations Geometric Series The Attempt at a Solution I split these up into two geometric series (infinity)sigma(k = 0) [2(1/3)^k] 2 / (1 - 1/3) r = 3 This diverges. (infinity)sigma(k = 0) (-1/5)^k...

This example appears in a set of notes entitled Geometric Algebra. I cannot follow the first half of the example. Is the reasoning incorrect. Thanks. Matheinste.

CASTEP Users?? Hi I am a beginer to castep. I am trying to do some geometric optimisations on various materials. The aim is to get familiar. Does anyone know of any tutorials available online other than the ones available in the tcm group cambridge. I would also like to interact and know...

This is the sequence: 1, 2, 5, 14, 41, 122 1. Is this a geometric series or an arithmetic series? 2. I know the formula is a sub n=[3^(n-1)+1]/2, but how do you get that from a sub n=a sub 1 * r^(n-1), which is the geometric formula for series.

I have a simple geometric proof (first proofs) I can't finish. Looks like this: A________L C________E suppose there's a straight line from l to c and a to e (to make an x) and a midpoint I. It says: Given I is the midpoint of both \overline{AE} and \overline{LC}; AE = LC Prove AI...