Questions tagged [inverse]

Questions on exact, symmetric reversal of a definition or functional mapping (i.e. the original form is returned when applied twice). Use this tag for issues on inversion of Mathematica expressions, or general inversion of math constructs.

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Invert a generic n x n matrix

I want to invert a generic n x n matrix. Is it possible to do this with Mathematica? Consider, as a minimal example, the $n\times n$ matrix: \begin{bmatrix}1n&0&...&0\\0&2n& ... &...
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Variation with respect to inverse metric in a Lagrangian density

I am trying to vary the following Lagrangian density with respect to the inverse metric appearing in the equation, but I am having trouble with how to write the right code in Mathematica. I have ...
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Inverting function variables

The original equation is a function of x. However, I want to invert the function and get an expression of x in terms of y. ...
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Inverse Function for an example

I have this funtion i would like to calculate the inverse Inverse[Sqrt[1 - Cosh[2 t] + a Sinh[2 t]]] a is positive number.
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InverseFunction fails at some parameter

Currently, I am faced with the difficulty of evaluating the inverse of the function below for certain negative decimal values of the parameter q. Specifically for ...
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2 answers
164 views

Plot the solution and Inverse as well

I used this code to solve an equation and now I would like to plot the solution with its inverse. I can't get some figures?!! ...
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1 answer
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Find an inverse function [closed]

this is probably a silly question, but how do I find an inverse function of y$ = a - b \cdot \text{ln}(1-\frac{x}{c})$? I tried doing $\text{exp()}$ on both sides but I don't know how to cope with $\...
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1 vote
1 answer
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Selecting the positive solution only

This my first problem on Mathematica and I'm working on version 13.0, and I want to get the inverse z transform for an equation, It works fine but it gives me the solution in the positive and negative ...
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2 votes
2 answers
114 views

ParametricPlot inside of ParametricPlot [closed]

I don't know why the following is not working! The code has a function y[x] then I have g[t] then I want to plot ...
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Integrate and InverseFunction

I solve an easy example to check that Mathematica can understand the difference between ArcTan and ArcTanh but as you see here I can't get Arctanh??!! Even I don't know why the inverse function is not ...
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Inverse VS Reduce

I got a solution I want to get inverse but it is not working in Mathematica or Rubi: ...
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A case for matrix multiplication (a.b).c unequal to a.(b.c) in mathematica 12.0.0.0, why?

The motivation of my calculation is to get the inverse for the following matrix ...
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How does Mathematica compute PseudoInverse? [closed]

What is the algorithm that is used in computing the PseudoInverse in Mathematica?
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Bayesian Linear regression (Ill-posed problem)

I want to use the ResourceFunction["BayesianLinearRegression"] from Wolfram function repository. With this function I want to solve the ill-posed problem $...
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Fail to inverse the Piecewise function embedded in a NDSolveValue

I am trying to estimate a function consisting of a Piecewise function that included in a FEM solver. I firstly developed my mesh for the FEM model based on @Tim Laska's work. The code is shown as <...
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Inverse Functions

I'm new to Mathematica, so I fell sorry for posting relativily naive/dumb questions. I have these two functions that represent X coordinate distortion of an SLA 3D printer. ...
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Simplification based on Kronecker Product Properties

I am trying to simplify some algebraically intensive expressions that involve inverses and Kronecker products. One simple example of such an expression is $$(1) \quad \quad \quad Z'(I_n\otimes\Sigma+Z\...
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3 answers
102 views

Does Solve make internally assumptions about the domain of the variables?

I recently tried to invert the innocent looking function $\frac{x}{(1+\sqrt{1-x})^2}$ So I tried the command Solve[x/(1 + Sqrt[1 - x])^2 == y, x], which ...
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Command to find the pre-image of a set that is mapped to by the function $f(x)=3^x \mod{17}$

$$f(x)=3^x \mod{17}$$ How to find the pre-image of the set if this function maps from real numbers to real numbers. What command would I use, to see the pre-image if the function would map from ...
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Inverse of the matrix with several indices

Suppose I have a square matrix $A_{mn}$ where $m=(i,j)$ and $n=(k,l)$. For example, if $i,j,k,l=1..N$ the matrix is $N^2\times N^2$. For simplicity, let me generate it by ...
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3 votes
2 answers
333 views

How to get x value where area under curve is some number?

My goal is to get x value where area under the curve (from the x ~ infinity) is about 0.05. But the code which I have tried shows errors. How to correct it? ...
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Getting inverse of x^2 with positive x

My goal it to get inverse of x^2 for positive x. But the result shows always minus -Sqrt[y]. How to correct ...
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Condition at Inverse function

My goal is to get inverse of -Log[1 - x]. But the result shows conditional expression. Could I know Why the condition -[Pi] <= Im[y] < [Pi] shows? There wass no assumption at variable y. ...
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Asymptotic expansion at infinity given a branch cut

Basically, I have obtained the function $\rho (r)$ below as a result of integrating $$\rho(r)=\int_{b_0}^{r}\frac{dx}{\sqrt{1-(b_{0}/x)^{1-q}}}$$ which results to ...
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How to return an inverse function based on parameters (for formal differentiation)

I want to return a different function for any given parameter in order to later calculate a value of the inverse of that function given the parameter as an indeterminate. That is, I want, for each $d$,...
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Plot Parametric f(x), inverse f(x) and f'(x) and then f(x)/f'(x) and inversef'(x)/inversef(x)

I want to plot f(x), inverse f(x) and f'(x) and then f(x)/f'(x) and inversef'(x)/inversef(x) f[x_] := 2 a ArcTanh[(# a)/Sqrt[-1 + #^2 b]] + a Log[1 + #^2 (a^2 - b)] - 2 Log[# b + Sqrt[-1 + #^2 b]] &...
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Plotting Inverse Function - more complicated [duplicate]

I would like to plot the inverse of $f$ using the same method that was suggested to me in my previous question: f[x_] := [(2 μ ArcTanh[(# μ)/Sqrt[-α + #^2 ν]] + μ Log[α + #^2 (μ^2 - ν)] - 2 Sqrt[ν]Log[...
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5 votes
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How to get an asymptotic of the real-valued branch of the inverse function?

Consider function $f:\mathbb R^+\to\mathbb R^+$, defined as $f(x) = x + x^2\left(1 + \log x\right)$. I need to find an asymptotic approximation of its inverse function $f^{\small(-1)}\!:\mathbb R^+\to\...
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1 answer
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InverseSeries slower than it should be

I am running into problems with InverseSeries taking far longer than it should. Given (for example) $$F = q + a_2 q^2 + a_3 q^3 + \ldots + a_{99} q^{99} + O(q^{100}),$$ Computing the inverse series is ...
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Series of inverse functions, unclear numerical constant

I was answering another question here and came up with this simple illustrative example that should have an analytic solution. Indeed it has, but I do not understand it. In particular, where 85 is ...
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-1 votes
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What is the inverse Jacobian of a 4D model? [closed]

For a Jacobian Matrix where the elements are represented as J11 J12 J13 J14 J21 J22 J23 J24 J31 J32 J33 J34 J41 J42 J43 J44 what is the inverse jacobian of this Matrix?
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12 votes
2 answers
540 views

InverseRadon behaves differently from iradon of MATLAB

I have to calculate a 2-dimensional radially symmetric distribution from a single projection. I know that InverseRadon should actually do the job, but I get the ...
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2 votes
0 answers
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Integration that involves inverse of a big symbolic matrix

I have a $300\times300$ symbolic matrix and I want to calculate its inverse matrix. It has been two days and Mathematica is still executing Inverse[T]. $T$ is the name of that matrix. Why am I ...
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2 votes
0 answers
41 views

establish matrix and inversion of a uppertriangularized matrix [closed]

Trying to create an uppertriangularized matrix with Poisson Distribution, find its inverse and multiply the inverse by a vector, i.e. ...
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3 votes
1 answer
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Inverse of DiracDelta at 0 is 99/5?

Here in this other question of mine I asked the question, but maybe here is more pertinent. When using Mathematica we can find the following result: ...
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1 vote
2 answers
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Finding the inverse of possibly non-invertible interpolation function

Consider the following sample code pts = Table[{i, i^2}, {i, -10, 10}]; foo = Interpolation[pts]; Plot[InverseFunction[foo][y], {y, 0, 10}] From the plot, we see ...
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0 answers
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Plotting CDFs of transformed normal random variables

I'm using the following transformed random variables ...
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1 answer
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How can I calculate this integral?

I would like to calculate the integral in equation pol[x] if the quantity is positive or negative. ...
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2 votes
1 answer
126 views

Numerically Inverting Characteristic Function with Inverse Fourier Transform

I'm trying to numerically invert this characteristic function: ...
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1 vote
1 answer
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InverseLaplaceTransform not working

I am trying to find the Inverse Laplace transform of a function I previously obtained from a Laplace transform, but the result obtained does not agree with the initial function. Why is this happening? ...
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3 votes
1 answer
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Inverse Laplace Transform how to find the exact solution

So I want to obtain a inverse Laplace transform from mathematica but I get this: How can I get the solution?
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0 answers
221 views

Inverse::luc Badly conditioned matrix may contain significant numerical errors. Why?

I want to find the inverse of the following matrix, which is given in terms of the following constants: ...
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1 vote
1 answer
134 views

Plot Arc Length Parametrization

I want to plot the parametrization of the curve with respect to arc length. It is all known that we have to find the inverse of the arc length of the original function i.e. $F(t)$, and ...
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2 votes
1 answer
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Inverse of matrix up to some order

Let $A(t,s)$ be a matrix of any size (potentially large), whose entries are polynomials functions wrt $(t,s)$ of order $N$. I would like to compute the inverse $X$ of $A$ up to the order $N$ that is $...
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3 votes
1 answer
453 views

Inverse Laplace transform of this complicated function

I have been solving a coupled PDE system analytically and I need to find the inverse Laplace transform of $(1)$ and get $T(x,y)$. $s$ is the Laplace domain variable and $\alpha, \beta, \gamma, T_{fi}, ...
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3 votes
2 answers
274 views

Strange NSolve failure [duplicate]

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1 answer
49 views

Issue With Example of Series Inversion

I am having a problem with the Mathematica InverseSeries command. Looking at the information page here, we have the following example; ...
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1 answer
142 views

Domain specifications for InverseFunction

I have difficulty implementing on how to specify the domain that I want for ry which is the inverse function of rho. The necessary condition is that, $\textbf{ry}$ must remain $\textbf{positive}$ for ...
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1 vote
3 answers
152 views

Inverting series with symbolic coefficients?

I am trying to invert the series symbolically. Is this possible in Mathematica? Example 1 - Let $p = u + au^2 + bu^3$, where $a,b$ are symbolic variables. I am trying to invert the series around $u=...
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Asymptotic solution of a second-order ODE containing InverseFunction

Essentially, I have a second-order differential equation given by ode below. In order to solve it, I need to obtain an asymptotic solution where $g(x)$ must vanish at infinity which will be used after ...
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