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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44 views

Don't understand results from solving polynomial equation [duplicate]

I attempting to solve an equation for x so that I may then switch x & y to get the inverse function. This is the code I have for solving for x: ...
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1answer
84 views

Propagation of error for not-analytical calculable inverse function

I have the function: gcsymb[Lpd_,a_,c_]:=1 /finv[1./Lpd^2,a,c]/Lpd with the definiton of finv: ...
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1answer
84 views

find the inverse of a hyperbolic function

Hi everyone I am new in Mathematica and I am trying to find the inverse of a function which contains hyperbolic tangents and I hope someone can help me. The function is y=(a)tanh(d(x-g))+ (a/2)(...
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1answer
60 views

InverseFunction of [E, 1, 1][c/Sqrt[K[1]]] isn't it just Log[c/Sqrt[K[1]]? [closed]

The problem is DSolve[E[del x'[t]/x[t]] x[t]^.5 == c, x[t], t] the answer is ...
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1answer
1k views

Inverse of a Digamma/ Polygamma Function

How one can find the inverse of a digamma/ Polygamma function in Mathematica 10?
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419 views

Approximate inverse of large sparse matrix with small diagonal element

I need to find inverse of a large sparse matrix with small diagonal element. I follow this question - Is there any way to obtain an approximate inverse for very large sparse matrices? and try to use ...
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0answers
468 views

Inverse of piecewise function with pieces invertible on specific domain

I have piecewise continuous function defined below: f=Piecewise[{ {15 + 1/6*(# - 3), # <= 27}, {# - 12 + 4 * Exp[-5/24*(#-27)], 27 < #} }]; This ...
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30 views

How to plot `y=y[x]` from `f[x_,y_]=f0` [duplicate]

Given a two-variable function f[x_,y_]:=(*complicated stuff in terms of x and y *) what I want is to do is Plot ...
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1answer
236 views

Creating Matrix,Inverted and Upper Triangulate inside Module

I was trying to fit this into a module but I didn't have any luck. And for some reason it won't Inverse the Matrix. Here's the code: Input: ...
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1answer
1k views

Symbolic matrix inversion

If I try to get an inverse of a matrix: a | b | c b | d | 0 c | 0 | 0 Inverse[{{a, b, c}, {b, d, 0}, {c, 0, 0}}] I get the answer: ...
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1answer
102 views

Interpreting Mathematica output or producing cleaner output [closed]

Could someone please explain what the following would look like in standard math notation (or explain to me what this means): ...
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79 views

Why are my 3D plots getting inverted? [closed]

For some reason, all 3D plots that I make in Mathematica 9 get inverted in both the image and the axes. For example, using the simple plot: ...
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2answers
703 views

How to reverse irreversible function in Mathematica?

How to reverse formula $y(x)=x (\frac{1}{sin \frac{\pi x}{2}})^\alpha$ i.e. express it as $x = x(y)$ in Mathematica? I did this way ...
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2answers
593 views

How can I get the inverse of my function?

The original function is $$f=\frac{1}{e^{\frac{\phi }{k t}}-1}-\frac{m+1}{e^{\frac{(m+1) \phi }{k t}}-1}$$ I want to express $e^{\frac{\phi }{k t}}$ about $m$ and $f$, so I tried: ...
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1answer
461 views

Inverting matrix with assumptions

I want to invert a matrix that contains some variables, so I thought I should give some assumptions to Mathematica to speed up the process. How do I assume that $s0,...,s8$ are positive constants ...
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1answer
68 views

Inverse KroneckerProduct given other arguments

I'm having problems working out how to do the inverse of a two argument Kronecker Product, given one of the decomposed column vectors. For example, say I have used the Kronecker Product on two ...
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0answers
640 views

How to invert a matrix with 100 trillion elements?

I have a $10^{7}\times 10^{7}$ matrix with the following properties: it is sparse it is gamma-5 it is almost Hermitian. If $M$ is the matrix we are trying to invert, we know $M=A M^{\dagger} A$ ...
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2answers
2k views

Get inverse of a matrix step-by-step [duplicate]

How can I get the inverse of a matrix step by step? An example: Given the matrix `{{8, 2}, {3, 2}}´, the result is {{$\frac{1}{5}$, -$\frac{1}{5}$}, {-$\frac{3}{10}$, $\frac{4}{5}$}}. But how can I ...
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2answers
230 views

Inverse of LogIntegral

I wanted the inverse logarithmic intgral, so I typed InverseFunction[LogIntegral] and received the expected symbolic answer. But when I try to integrate it or ...
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2answers
419 views

Block matrix definition and inversion

I would like to define the following block matrix $$ A=\begin{bmatrix} H-G_1 & -G_1 & \ldots & -G_1 \\ -G_2 & H-G_2 & \ldots & -G_2 \\ \vdots & \ldots & \vdots & ...
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1answer
694 views

Is there an inverse function for F[x] = {Cos[x], Sin[x]} in Mathematica?

Mathematica has functions ArcCos, ArcSin, and ArcTan, but none of these does what I need, ...
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1answer
294 views

In there a way to derive the inverse value of CDF format MultinormalDistribution?

Is there a way to produce the inverse value of multinormal distribution function in CDF format with 0.05 significance level? I found the function called ...
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1answer
287 views

Fit to inverse function

I am trying to fit my data to an inverse function from solving a DGL: ...
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1answer
440 views

Solution to a T+U = E equation

I needed to solve really easy differential equation (in dimensionless units): $$ \mathcal{T} (\dot{\xi}) + \mathcal{U} (\xi) = \text{const.} \equiv \varepsilon ; \quad T(\dot{\xi}) = \dot{\xi}^2 ; \...
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2answers
303 views

What would be the inverse function for the following condition?

I tried the problem but i couldn't take above condition in question in terms of f(x)
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1answer
434 views

Inverse of a restriction of a non-invertible matrix

Let $A∈R^{4×4}$ be a non-invertible matrix, with $2$-dimensional kernel. How can I compute the inverse of the restriction of $A$ on a subspace where it is invertible: $A^{-1}v \,\,\,\,$ where $\,\,\,\...
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1answer
235 views

Inverse functions - how are they calculated?

Mathematica is able to calculate InverseFunction[LogIntegral] and InverseFunction[RiemannR] (and many other inverse functions). ...
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1answer
1k views

Specific entry of inverse of large matrix

Given a large (say 10x10) sparse Hermitian matrix with symbolic entries, I need four specific entries of the inverse matrix. It seems wasteful to me to compute 100 entries of which I only need a few ...
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1answer
2k views

How to find the inverse a symbolic matrix that Mathematica thinks might be singular

I have a square matrix depending on a parameter "a". When "a" has a numeric value (eg 2.1 * 10 ^ 8) through the inverse function Inverse[] I can invert the matrix. If I write the matrix as a function ...
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0answers
405 views

Speeding up inversion of symbolic matrices by invoking caching

Is it possible to reduce the computation time taken to find inverse of symbolic matrices USING CACHING TECHNIQUES accessible (if any)? I am trying to compute inverse of symbolic matrices of size ...
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0answers
83 views

How to Invert a Multivariate Interpolating Function? [duplicate]

I used NSolve on a partial differential equation with boundary conditions to get a numerical solution that Mathematica says is of the form InterpolatingFunction. I then defined a function f(x,y) which ...
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1answer
220 views

invert system of two parametric ODEs and plot results of do-loop

I can solve this system of parametric ODE (u is the parameter,while g,e and ...
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1answer
812 views

How to do Inverse formulas/Rearrange formulas in Mathematica? [duplicate]

Hi am a student in chemical engineering and I have the necessity to rearrange formulas algebraically, for example ...
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0answers
392 views

Invert a transcendental function

I have tried Reduce and Solve in Mathematica, as well as have a long list of tries in Maple, but cannot seem to get anywhere ...
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1answer
552 views

Finding the InverseFunction of a polynomial function restricted to an interval [duplicate]

I want to calculate the inverse of f[x_] := 1/2 - (x (4 x^2 - 9))/12 /; -1/2 <= x <= 1/2 f[x] is monotonic inside $-0....
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1answer
117 views

InverseFunction oddity

InverseFunction[ConditionalExpression[#, 0 <= # <= 1] &] InverseFunction[ConditionalExpression[#, -1 <= # <= 1] &] The first line produces ...
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2answers
1k views

Is there a way to symbolically invert a piecewise function

I have a piecewise function that is continuous and strictly monotonic, like this: f[t_] = Piecewise[{{t/4, t < 0}, {t/2, t < 3}, {3/2 + (t - 3)*3, True}}] ...
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1answer
2k views

Invert Colors Stylesheet White on Black

There have been a couple studies done that showed that white text on a black background increase recall of data. Although this is certainly debatable how might I invert the colors of Notebook font ...
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1answer
187 views

Need a generalization of RootApproximant to recognize linear combinations over algebraic numbers

RootApproximant does a very good job when I need to recognize an algebraic number and when enough of its digits are known (or even when an unlimited number of ...
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1answer
553 views

Inverse on a restricted domain

I have a function, whose domain is [0,1]. The function is f = Piecewise[{{Exp[-β * (-Log[#])^α], 0 < # <= 1}}, #]& with ...
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1answer
1k views

InverseFunction on an Interpolating Function is misbehaving

I am getting strange behavior when I try to calculate the inverse of an interpolating function for two similar data sets. My data sets are: ...
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1answer
1k views

Prandtl-Meyer function

I'm trying to solve for Mach number based on the given Prandtl-Meyer function, however I keep getting odd error. Here is my code: ...
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5answers
3k views

Plotting the solutions to a transcendental equation

I am trying, to no avail, to use Mathematica to produce a plot in (x, y)-space of the solutions to the equation Cos[Sqrt[y]] + Sin[Sqrt[y]]/Sqrt[y] == Cos[x] ...
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1answer
2k views

Efficient method for inverting a block tridiagonal matrix

Is there a better method to invert a large block tridiagonal Hermitian block matrix, other than treating it as a ordinary matrix? For example: ...
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1answer
1k views

How to get the determinant and inverse of a large sparse symmetric matrix?

For example, the following is a $12\times 12$ symmetric matrix. Det and Inverse take too much time and don't even work on my ...
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0answers
603 views

Automatic inverse for Lambert’s Azimuthal Equal-Area Projection

I’m interested in finding closed-form inverses for map projection equations in general (of course, this is not always possible). I’m hoping Mathematica can help me with some of the trickier ones. As ...
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3answers
1k views

How can I solve Tan[t] - t == F[x] for t as a function of x?

How can I solve the equation Tan[t] - t = Ax, where A is a constant for t[x]? I know that ...
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1answer
858 views

Find an inverse matrix, regarding a parameter as real

I have the matrix ...
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2answers
5k views

How to convert a system of parametric equations to a normal equation?

For example, I have a system of parametric equations (R is a constant number) : ...
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0answers
1k views

Inverse Laplace transform not obtained

I can't seem to be able to compute the inverse Laplace transform of a Laplace transform: ...