Inverse Definition and 1000 Threads

Hi, If A is some nonsquare matrix that is possible rank-deficient, then am I right to understand that (A^T)(A) is a positive semidefinite matrix? Does there exist an inverse (A^T A)^-1? Thanks for any help

Is $F^{-1}(F(E))\cap E=E$? Thanks!

Homework Statement Find the inverse laplace transform of (2/(s+2)^4) using the given table of identities: Homework Equations Here are the given identities: The Attempt at a Solution Alright, I realize that there is a simple identity that I can use with a factorial symbol, but this...

This is a conceptual question on the region of convergence (ROC) and the inverse Laplace transform (ILT). Here the bilateral laplace transform (LT) and the ILT are given by F(s)=L\{f(t)\}=\int_{-\infty}^{+\infty} f(t) e^{-st} dt and f(t)=L^{-1}\{F(s)\}=\frac{1}{i...

Homework Statement Find the inverse function of y= x/2 - 5/2x Homework Equations The Attempt at a Solution I've tried to manipulate the equation to find x(y) without any sucsses.

Homework Statement For a physics problem I must take the inverse Fourier transform of 2 functions. Namely I must compute the integral ##\frac{1}{\sqrt{2\pi}}\int_{-\infty} ^\infty [A\cos (ckt)+B\sin (ckt)]e^{ikx}dk##.Homework Equations Already given. i is the complex number. t is greater or...

Homework Statement Find (X * Y-1)T - (Y * X-1)T When X = [3 5] .....[1 2] and Y = [3 4] ...[2 3] Homework Equations Inverse= 1/ad-bc [d -b] ......[-c a] The Attempt at a Solution I got: [9 -6 ] [14 -9] But the answer is: [-3 -2] [6 3]I did the problem twice and got the same answer so I...

Finding the inverse of a function? Homework Statement Find (f^-1)'(a), a =2 √(x^3 + x^2 +x +1) So, if a = 2, then f^-1(2) = 1 and f(1) = 2 Homework Equations The Attempt at a Solution I figured out that f(1) = 2, so √(3(1)^2 + 2(1) + 1) = √6 so the...

Hello, This is not a homework exercise, so I decided to post it here. Hopefully one of you could help. I would like to find an explicit expression for (I-A)^(-1), provided that A is a squared matrix (nxn) and A^k = 0. It is also given that I-A^k = (I-A)(I+A+A^2+...+A^(k-1)). I understand that by...

For any A \in \mathcal{R}^{n \times m}, does A^T A have an inverse? From the wikipedia article for transpose ( http://en.wikipedia.org/wiki/Transpose ), I found that A^T A is positive semi-definite (which means for any x which is a column vector, x^T A^T A x \ge 0 ). And the Wikipedia article...

I tried posting this at stack exchange but it never got the question answered. I want to prove this: If f:U→C is holomorphic in U and invertible, P∈U and if D(P,r) is a sufficently small disc about P, then f^{-1}(w) = \frac{1}{2\pi i} \oint_{\partial D(P,r)}{\frac{sf'(s)}{f(s)-w}}ds

Hello, Would it be correct to say that if for every two different vectors x and y, A*x ≠ A*y (where A is a symmetrical matrix), then A is NOT necessarily invertible? In other words, albeit for any two different vectors x and y symmetrical matrix A times one of the vectors is not equal to A...

Hello everyone! I have three questions: (1) If $x\in R$, is it true that $f ^{-1} (f(x)) = x$? (2) If $y\in R$, is it true that $f (f^{-1}(y)) = y$? (3) If $B\subset R$, is it true that $f(f ^{-1} (B)$? I think I have showed it for (3), but not sure of my proof. For (1) and (2), I considered...

I am currently doing a trig question and trying to find the location of the acute angles of cosine inverse and I am just wondering if cosine inverse follow the cast rule? In other words would it be positive where cos would be positive or not?

Hi, all I am looking into inverse cosine operations. I have a question like follows: Let x and y be two variables of degrees, how to separate equation arccos(x+y) into an equation that contains x and y separately? Such as arccos(x+y) = f1(...x) + f2(...y)? Thank you very much for your...

The Title pretty much says it all. I'm trying to learn how to solve the Inverse Laplace Transformation of Arctan(s/2). An equation of this sort was not explicitly covered in class and I'm having difficulty figuring where to start to solve it. If anyone could give me a general idea that would...

Hi Does anyone know if there is a relation between the Fourier transform of a function and the Fourier transform of the inverse function in summary FT[f(x)] ?= FT[f-1(x)] Thanks!

Homework Statement There were other questions before this one but i solved them all. Find the inverse function of f(x)=arctan(\sqrt{1+x^{2}}-x) for every x in the interval ]0,pi/2[ .That's the interval that I found when counting f(R) because f is a bijection from R to f(R). Hence...

Homework Statement How to solve part (iv) & (v)Homework Equations general form : y = a(x-h)^2 + kThe Attempt at a Solution In part (iv) for finding domain and range I converted g(x) in general form and then compared it with general form.

Treatment originally used to discard inverse square law as solution to Olbers' paradox was not set up correctly. If we include sensor (camera) in the treatment and model light as photons the result describes what we actually see.

Homework Statement I need to expand 1/y(x)2 , where y(x)=x1/2Ʃ(-1)n/(n!)2 * (3x/4)n for n=0 to ∞ Homework Equations How does one arrive at the correct solution (-coefficients seem to vanish, only + remain)? The Attempt at a Solution I know that x1/2Ʃ(-1)n/(n!)2 * (3x/4)n expands...

I can't seem to make head or tail of the description of direct and inverse limits of abelian groups in problems 8 and 10 of the attached excerpt from Dummitt and Foote. Does anyone have a simpler or more intuitive definition of these two notions, or just an explanation of Dummit and Foote's...

Homework Statement This is a practice problem for a test on Laplace transforms Find L^-1[ (9s^3+17s^2+66s+45) / (s^2+9)(s+2)^2 ] (L^-1 = inverse laplace transform) Homework Equations From Laplace transform tables: L^-1[ 1 / s-α ] = e^αt L^-1[ s / s^2+ω^2 ] = cos(ωt)...

Homework Statement Assume the function f defined by f(x)=5x+sin(πx) is strictly increasing on ℝ. Find (f^{-1})'(10) Homework Equations Let I and J be be intervals and let f:I->J be a continuous, strictly monotone function. If f is differentiable at c and if f'(c)≠0, then (f^{-1}) is...

Does inverse square law apply to light in vacuum?

Hi, I'm specifically trying to compute (VΔYT)-1, where V is nxn and orthogonal, Δ is diagonal, and Y is nonsingular. In general we have (AB)-1 = B-1A-1 But how do we do this in general for many matrices? Is there a method, and as long as the matrix dimensions agreed, does the...

f is a one to one function with inverse f^-1, and we are asked to find the inverse of s(x)=[1+f(x)]/[1-f(x)] My attempts leave me with s^-1(x)= [f^-1(1-x)]/[f^-1(-x-1)] and I don't think this is correct. I can't find any examples of problems like this online.

Why is Baye's theorem called "inverse prob"? What is the reason for calling Baye's theorem as "inverse probability"? Any valid reason? Thanks a lot

I am having trouble with this homework problem, I know how to get started but I just don't know how to carry through the completion of the problem: Question: Given the Fourier transform of an aperiodic signal X(ω) = 2*sin(3(ω-2π))/ω-2π (a)find its inverse Fourier transform x(t) using...

so here's the question: if you have some equation relating a function, f(x), and its inverse, f-1(x), can you solve for the function? for example, solve for f(x): f(x)+f-1(x)=x^2 how about: f(x)+f-1(x)=g(x) my math teacher (AP calc) was stumped on this one... any thoughts?

I have to take the inverse laplace transform of the above function. Now, I know that I can factor (s^2+5s+6) as (s+3)(s+2) and take the easy way out. However, I did it as above on a test, getting A = -1, B = -1, and C = 1. I then took the inverse laplace transform and got something involving...

hi there I'd like to show that the sphere \mathbb{S}^n := \{ x \in \mathbb{R}^{n+1} : |x|=1 \} is the one-point-compactification of \mathbb{R}^n (*) After a lot of trying I got this function: f: \mathbb{S}^n \setminus \{(0,...,0,1)\} \rightarrow \mathbb{R}^n (x_1,...,x_{n+1})...

Homework Statement Prove in general that if m does not equal n, then AB and BA cannot both be identity matrices, where A is mxn and B is nxm. Homework Equations None (that I know of at least). The Attempt at a Solution At first I thought it would be a good idea to define each...

Homework Statement Prove that if the inverse of a function between topological spaces maps base sets to base sets, then the function is continuous. Homework Equations The Attempt at a Solution I really don't know how to do this. Wikipedia entry for 'base sets' redirects to Pokemon...

First of all, I'm 13 so I might not comprehend the complex vocabulary or symbols others might use. Second, I just joined! Okay, let's get to it. I think I know what the inverse square law is: if a number goes up by x, then the other number is the square of x but in the negative side...

Homework Statement Simplify the following expression: arccosh \left(\frac{1}{\sqrt{1 - x^2}}\right) \forall x ∈ (-1, 1) Homework Equations cosh(u) = \left(\frac{1}{\sqrt{1 - tanh^{2}u}}\right) u ∈ ℝ The Attempt at a Solution x = tanhu ∴ u = arctanhx u ∈...

Homework Statement find the partial fractions and thus the inverse of the following 6s^2-2s-11/(s-1)(s^2-1) and 7s^2+8s+16/(s+2)(s^2+3) Homework Equations answer tutor gave for the fist one was 3e^2t + 3cosht + sinht and second was 4e^-2t+3cos sqrt3t+ 2/sqrt3 sin sqrt3 The...

I am trying to find a real life inverse linear transform which can be used to motivate students. Does anyone have an example or two? I am looking for an example which will have a real impact. Thanks in advance.

I am trying to find a real life inverse linear transform which can be used to motivate students. Does anyone have an example or two? I am looking for an example which will have a real impact. Thanks in advance.

I understand that given two functions f:X→Y and g:Y→X, to say that f is the inverse function of g means g o f:X→X is defined by g(f(x))=idx and to say g is the inverse function of f means f o g: Y→Y is defined by f(g(x))=idy I understand how to find inverses of one variable functions and...

Homework Statement f(x)=e^x^2 f^(-1)(x)=? 2. The attempt at a solution i reversed x and y so i got x=e^y^2 ln both sides to get lnx=y^2 so (ln(y))^(1/2) what am i doing wrong?

Homework Statement Consider f(\vec{x}) = |\vec{x}|^r, where \vec{x} \in ℝ^n and r \in ℝ. Find \vec{∇}f The Attempt at a Solution I know a vector function maps real numbers to a set of vectors, but here I believe we have the opposite. (inverse of a vector function, assuming inverse...

Hello Everybody. I have a rather simple question, which still kept me thinking for two hours without any result. If we want to determine the multiplicity in the microcanonical ensemble we just divide the volume of the shell containing the accessible microstates over the volume of one...

Hello if y \propto 1/x would 2y \propto 1/0.5x or 2y \propto 1/2x thank you for any replies

Given a Finsler geometry (M,L,F) and $$g_{ab}^L=\frac{1}{2} \frac{\partial^2 L}{\partial y^a \partial y^b}$$ $$g_{ab}^F=\frac{1}{2} \frac{\partial^2 F^2}{\partial y^a \partial y^b}$$ $$F(x,y)=|L(x,y)|^{1/r}$$ I manage to get the following form $$g_{ab}^F=\frac{2|L|^{2/r}}{rL}(...

I have been struggling to find an inverse to a Lorentz matrix \Lambda using formula: \Lambda^{-1}= \frac{1}{| \Lambda| }\textrm{adj}(\Lambda) from linear algebra. \Lambda = \begin{bmatrix} \gamma&0&0&-\beta \gamma \\ 0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0\\ -\beta \gamma & 0 & 0 & \gamma...

Hello everyone! I'm struggling to find a general formula for obtaining an inverse of a symmetric matrix, for e.g. 1 i -1 i -i 2 -1 2 1 Any help is appreciated!

I'm reading the first chapter of Topology by Munkres. There we can see: "if f is bijective, there exists a function from B to A called the inverse of f . (...) As another situation where care is needed, we note that it is not in general true that f^{-1}(f(A_0) = A_0 and...

I want to perform the inverse of \frac s { [(s+α)^2-β^2](s^2+ω^2)} I know the conventional way is \frac s { [(s+α)^2-β^2](s^2+ω^2)}= \frac{As+B}{[(s+α)^2-β^2]}+\frac{Ds+E}{(s^2+ω^2)} s= (As+B)(s^2+ω^2)+(Ds+E)[(s+α)^2-β^2] \Rightarrow\; A+D=0,\; B+E+2\alpha...

Homework Statement When a camera flashes, the batteries begin recharging the flash capacitor which stores the charge Q according to the function Q(t) = Q* (1-e-t/a) where t is the elapsed time in seconds since the camera flash and Q* and a are non-zero (a) What does Q* represent? (b) Find the...