# 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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### 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: ...
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: ...
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)(...
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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### Inverse of a Digamma/ Polygamma Function

How one can find the inverse of a digamma/ Polygamma function in Mathematica 10?
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### 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 ...
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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### 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 ...
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: ...
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: ...
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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### 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: ...
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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### 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: ...
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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### 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 ...
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 $M=A M^{\dagger} A$ ...
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}}Ā“, the result is {{$\frac{1}{5}$, -$\frac{1}{5}$}, {-$\frac{3}{10}$, $\frac{4}{5}$}}. But how can I ...
230 views

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 ...
419 views

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### 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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### InverseFunction oddity

InverseFunction[ConditionalExpression[#, 0 <= # <= 1] &] InverseFunction[ConditionalExpression[#, -1 <= # <= 1] &] The first line produces ...
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}}] ...
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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### 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 ...
553 views

### Inverse on a restricted domain

I have a function, whose domain is [0,1]. The function is f =Ā Piecewise[{{Exp[-Ī² * (-Log[#])^Ī±], 0 < # <= 1}}, #]& with ...
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### 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: ...
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: ...
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] ...
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: ...
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 ...
603 views

### Automatic inverse for Lambertās Azimuthal Equal-Area Projection

Iām interested in finding closed-form inverses for map projection equations in general (of course, this is not always possible). Iām hoping Mathematica can help me with some of the trickier ones. As ...
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### 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 ...
858 views

### Find an inverse matrix, regarding a parameter as real

I have the matrix ...