Inverse Definition and 1000 Threads

Homework Statement I have a function f:M_{n×n} \to M_{n×n} / f(X) = X^2. The questions Is valid the inverse function theorem for the identity matrix? It talks about the Jacobian at the identity, but I have no idea how get a Jacobian of that function. Can I see the matrices as vectors and...

Hi there! I'm back again with functions over matrices. I have a function f : M_{n\times n} \to M_{n\times n} / f(X) = X^2. Is valid the inverse function theorem for the Id matrix? It talks about the Jacobian at the Id, but I have no idea how get a Jacobian of that function. Can I see that...

By considering the product of complex numbers: z = (2+i)(3+i) Show that \tan^{-1}\frac{1}{2} + \tan^{-1}\frac{1}{3} = \frac{\pi}{4}

Hey guys. In a project I'm working on, it would be very convienent to express the inverse of this matrix in terms of its size, NxN. The matrix is \leftbrace \begin{tabular}{c c c c} a & b & \ldots & b \\ b & a & \ldots & b \\ b & b & \ddots & b \\ \vdots & vdots & ldots & b \\ b...

Homework Statement f(s) = 6/s^2-9 Homework Equations I think f(t) = (1/b-a)(e^-at-e^-bt) The Attempt at a Solution Replace 6/s^2-9 with 6/(s-3)(s+3) a=-3 b=3 Plug in (1(6)/3-(-3))(e^-(-3)t-e^-3t) Final Result e^3t-e^-3t

Homework Statement f(s) = -5s/S^2+9 Homework Equations I think f(t) cosωt = f(s) s/s^2+ω^2 The Attempt at a Solution ω=3 Answer -5cos(3t) Can anyone tell me if I did this correctly? I think I did but just want to make sure, if not can you tell me what I did wrong? Thanks

Solve the following system of equations using the inverse of the coefficient matrix, 2x + 4y = -9 -x - y = 2 My attempt- [2 4 [x = -9 -1 -1] y] = 2 |A| x b |A| = -2-4=-6 [x = 1/-6 [-1 -4 [-9 1/-6 [ 1 = 0.03 y] = 1...

When thinking of a spherical shaped particle moving about under Brownian motion, one describes its motion by Diffusion. The units being \frac{m^2}{s} I can understand this physically as a distance it will travel from a certain point in space averaged over x-y and z direction. Now rotational...

Hi everyone, :) An interesting question I thought about recently. Is it true that a Latin Square of integers (or real numbers) treated as a matrix is always invertible? If not can anybody give a counterexample. I think latin squares are invertible but I am unable to prove it. Hope you can help...

Hello, This is the thread I originally wanted to respond to, but it's closed: https://www.physicsforums.com/showthread.php?t=650126 I also found this on Wiki-talk page, which seems to be the same argument...

Homework Statement This was in my test paper today: A transformer is cut into half so that one half contains the primary coil and the other half contains the secondary coil. They are moved 30cm apart. Explain why the transformer would not work The Attempt at a Solution My answer: The magnetic...

Homework Statement Problem One: Two kilometres away from a point source of infrared waves, the intensity is 4 Mw−2. Calculate the intensity 1m away from the source. Problem two: Light from a candle has an intensity of 20.0 units when a meter is placed 3.0m away. What is the reading on the...

I usually see that Laplace transform is used a lot in circuit analysis. I am wondering why can we know for sure that the Laplace and its inverse transform always exists in these cases. Thank you.

I'm learning AC and theory says that the polarity of AC inverses.. even the name says 'alternating current'.. now what about the live and neutral? does the current goes from neutral to live and and vice versa? Some people says that only the phase inverses, but the current is always from live to...

Hi, this is not a homework and my problem is much bigger for me to give full details here. I came across this integral \mathcal{I}(\xi)=\int^{\xi_c}_{\xi}{\rm d}\xi^\prime\exp\left[\sqrt{2}\sigma\,{\rm Erf}^{-1}\left(1-\frac{8\pi}{3}{\xi^\prime}^3\right)\right] where Erf^{-1} is the...

Homework Statement I had a question in my midterm, it was to find inverse laplace tansform of: (4s+5) / (s^2 + 5s + 18.5) Where ^ denotes power. Homework Equations The Attempt at a Solution My answer was to find the complex roots of equation (s^2 + 5s + 18.5) , by them...

Given a trig equation, like: sin(x)² + cos(x)² = 1² or sin(x) = 1/csc(x), exist a correspondent inverse: arcsin(x) + arccos(x) = π/2 and arcsin(x) = arccsc(1/x), respectively. Thus, given an any trigonometric equation, how find its correspondent inverse?

In an AC circuit, we know that the polarity inverses, and what i know is that the flow of current also will therefore inverse.. which means that the live will become negative and the neutral will become positive.. What i can't understand is how the polarity inverses but the live is still the hot...

Why is e^-1 the inverse of natural log e? Thank you

f: (R*R)->R f(x,y)=x+y if I'm asked to write 2 right inversed fanctions of f. can I say that: f1: R-> (R*R) f1(x)= (x-1, 1) f2: R-> (R*R) f1(x)= (x-2, 2) because: f(f1(x))= f(x-1,1)=x-1+1=x well this does matches the definition of right inverse function but what bothers me I guess is...

Watching this video http://youtu.be/1JnayXHhjlg?t=5m30s, I understood the ideia the Fourier transform, that is a continuous summation of sinusoids. But now If I have amplitude and phase as function of σ and ω, the summation wouldn't be ##\sum_\sigma \sum_\omega A_{\sigma \omega} \exp(i...

f^-1 (E^c) = (f^-1(E))^c where f is map from X to Y and E is in Y. Prove equality is true.

can you check if my solution here is correct. If not can you tell me how to do it properly. thanks!

Homework Statement Problem: Given C is the graph of the equation 2radical3 * sinpi(x)/3 =y^5+5y-3 Homework Equations (1) Prove that as a set C= {(x,y) Exists at all Real Numbers Squared | 2radical3 * sinpi(x)/3 =y^5+5y-3 is the graph of a function differentiable on all real...

Homework Statement Let f be a function defined as f:(0,exp-3/2) → [-1/4, ∞), f(x) = (ln x)^2 + 3 ln x + 2 then inverse of f is equal to The Attempt at a Solution The two possibilities are exp (\dfrac{-3\pm\sqrt{4x+1}}{2}) How to decide which one is correct?

Say for some general function f(x), and g(x) = ∑x=0∞ f(x) (assuming function is defined) Is there a way to find the zeroes of g(x)? Is there any relationship between the zeroes of f(x) and g(x)? Sorry if this question is poorly asked, i just began learning about summations and infinite series...

Hi I am facing a mathematical problem in my research. I am not a maths magor and i need to do this to move on with my research. Please check the picture for the equation http://i.stack.imgur.com/jQroR.jpg Mod note: Image was too large, so deleted it, and replaced it with LaTeX. Left the...

I'm hoping that you can help me settle an argument. For a matrix \textbf{M} with elements m_{ij}, is there any sitaution where the notation (M_{ij})^{-1} could be correctly interpreted as a matrix with elements 1/m_{ij}? Personally I interpret (M_{ij})^{-1} in the usual sense of an inverse...

Homework Statement ln(sec^-1(3x^2 +1)) Homework Equations The Attempt at a Solution 1/sec-1(3x2+1) * 1/(3x2+1)(sqrt(3x2+1)2-1) * 6x Is this correct ?, do I just simplify from here ?

Homework Statement Find the inverse Laplace transform of F(s)=5e^(-8s)/(s2+36) Homework Equations The Attempt at a Solution I know that to find the inverse Laplace transform of this function, I start by factoring out (e^(-8s)) to end up with 5/(s^2+36), and that my final answer...

Obtaining the Equation of a Path I'm working on a project for myself in SolidWorks which involves a scissor-type mechanism. The bottom ends of the linkages are attached to disks that are free to rotate around the central hub where all the gears are attached. On the other side of the hub is...

is it true that \frac{1}{g_{ab}}=g^{ba}? I am a bit confused by the index notation. I especially wonder about the inversion of the indices. Could somebody clarify this please?

Homework Statement Take the inverse Fourier Transform of 5[\delta(f+100)+\delta(f-100)]\bigg(\frac{180+j2\pi f*0.0135}{1680+j2\pi f*0.0135}\bigg)Homework Equations g(t)=\int_{-\infty}^{\infty} G(f)e^{j2\pi ft}dt The Attempt at a Solution g(t)=\int_{-\infty}^{\infty}...

an S-shaped lawn sprinkler (an S-shaped pipe on a pivot) in which water squirts out at right angles to the axis and makes it spin in a certain direction is taken and if you had a lake, or swimming pool (a big supply of water) and you put the sprinkler completely under water, and sucked the water...

Homework Statement The intensity (I) of sunlight (the received power per unit area) drops with distance (d) from the sun according to the inverse square law - i.e I2/I1 is proportional to (d1/d2)^2 What is the total power received at Earth (above the atmosphere) per unit of surface area...

Digging in the wiki, I found this relation between 'arc-functions' and 'arc-functions-hyperbolics" \\ arcsinh(x)= i \arcsin(-ix) \\ arccosh(x)= i \arccos(+ix) \\ arctanh(x)= i \arctan(-ix) https://it.wikipedia.org/wiki/Funzioni_iperboliche#Funzioni_iperboliche_di_argomento_complesso...

Homework Statement I have to find ##\tan^{-1}(2i)##. Homework Equations The Attempt at a Solution So far I have ##\tan^{-1}(2i)=z\iff tan z= 2i\iff \dfrac{sin z}{cos z}=2i ##. From here I get that ##-3=e^{-2zi}##. I do no know how to take it further to get ##z=i\dfrac{\ln...

A family of functions is a set of functions that share one or more properties. ie: The family of quadratics with zeros 1 and 10, or the linear functions with a slope of 20. there is a family of linear functions where each member is its own inverse. What linear property defines the family? (I...

The function y = x is its own inverse. Why?

I found this forum on Google. This may not be the right section so excuse me if so. I have a rather simple question though. When you take a magnifying glass on a sunny day and position it just right over a piece of paper, the paper will start to burn. Is the inverse square law (distance) the...

Trying to see the logic in deriving length contraction and time dilation using the Lorentz transformations and inverse Lorentz transformations. In the following treatise it leads to ambiguities. Given ##Δ\acute{t}=\gamma(Δt-\beta c^{-1}Δx)## (1) ##Δ\acute{x}=\gamma(Δx-\beta c Δt)##...

1. Given: The DTFT over the interval |ω|≤\pi, X\left ( e^{jω}\right )= cos\left ( \frac{ω}{2}\right ) Find: x(n) 2. Necessary Equations: IDTFT synthesis equation: x(n)=\frac{1}{2\pi}\int\limits_{-\pi}^{\pi}X\left ( e^{jω} \right ) e^{j\omega n}d\omega Euler's Identity...

If given an one-form like: ##\omega = u dx + v dy##, dω is ##d\omega = \left ( \frac{\partial v}{\partial x} - \frac{\partial u}{\partial y}\right )dxdy##. So, is possible to make the inverse path? Given: ##d\omega = Kdxdy## , which is the expression for ω ? ##\omega = ? dx + ?dy##

Homework Statement Find the inverse Fourier transform of f(w)=1 Hint: Denote by f(x) the inverse Fourier transform of 1 and consider convolution of f with an arbitrary function. Homework Equations From my textbook the inverse Fourier transform of f(w)=\int F(w)e^-iwt dw The...

To start with, let's work on the Partial Fraction decomposition. $\displaystyle \begin{align*} \frac{A\,s + B}{s^2 - 16s +128} + \frac{C\,s + D}{s^2 + 16s + 128} &\equiv \frac{3s}{s^4 + 16\,384} \\ \frac{ \left( A\,s + B \right) \left( s^2 + 16s + 128 \right) + \left( C\,s + D \right) \left(...

Hi there, Let S denote the shift operator on the Hardy space on the unit disc H^2, that is (Sf)(z)=zf(z). My question is to show the following identity (1-\lambda S^*)^{-1}S^*f (z)=\frac{f(z)-f(\lambda)}{z-\lambda}, where \lambda,z\in\mathbb{D} Thanks in advance

How do I find all the possible ROC for a transfer function written as \[ H(s) = \frac{(s - 2)^{n_1}}{(s + 2)^{n_2}(s + 1)^{n_3}(s - 1)^{n_4}} \] where \(n_i\in\mathbb{N}\).

With a Laplace transform, we can remember common set ups; for example, \[ \mathcal{L}\{e^{-at}\} = \frac{1}{s + a}. \] When it comes to the inverse Laplace transform, I can only find the tables to remember in a book. However, if we go back to the Laplace transform, we can always do \[...

I am having difficulty understanding the following problem. I feel it should be very simple but am unsure how to interpret it. A relation ##R## is defined on ##N## by ##aRb## if ##\frac{a}{b} \in N##. For ##c, d \in N##, under what conditions is ##c R^{-1} d##? (Exercise 8.6 from Chartrand...

Please see attached. I am not sure whether my example of this function is correct. f(x) = ##sin(\frac{\pi x}{2})## obviously, f(x) is continuous on [-1,1] and differentiable on (-1,1) Inverse of f(x) will be ##\frac{2 sin^{-1}x}{\pi} ## and d/dx (inverse of f(x)) will be ##\frac{2}{π...