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.

123 questions
182 views

Is there a built-in function to inverse Thread?

Namely, while Thread @ f[{a, b}, {x, y}] gives {f[a, x], f[b, y]} the InverseThread (if it existed) should reverse the ...
135 views

Treat symbols as elements of a non-commutative field

I want to invert a matrix, {{a,b},{c,d}}, where a,b,c,d are elements of a non-commutative field (for example invertible matrices)...
170 views

Inverse Function in Mathematica

How to find bConst in the following code ...
69 views

Solving for $\beta$ in $\tan\gamma = C \tan\beta$, $0 \leq C \leq 1$, where $\beta$ must be in same quadrant as $\gamma$

I am pretty weak with Mathematica, so please, nothing overly complicated. The ArcTan[x, y] function allows for a full range of $2 \pi$ in the output. However, for ...
84 views

Finding input of the function $f(a,b,c) = (d,e)$ such that $|d-e|$ = constant for $d\in[d_0,d_1]$

The actual question contains a few more parameters than mentioned in the title, but the idea will remain very similar. Lets begin abstractly; I have a certain function $f(a,b,c) = (d,e,g,h)$. I am ...
518 views

Why doesn't Lambert function (ProductLog) simplify?

I have Simplify[ProductLog[x*Exp[x]]] By the definition of the Lambert function, this should be simply x. But Mathematica outputs this: ...
148 views

How to invert an Elliptic function where the elliptic nome is a function of an independent variable?

I have a Jacobian elliptic function as a function of two independent variables $x$ and $y$. The elliptic parameter $m=m(y)$, $0 \leq m \leq 1$, is also a function of the variable $y$, and thus the ...
379 views

Implicitly inverting a function from numerical solution [closed]

I have the following piecewise continuous function: ...
115 views

Function inversion [closed]

I have an expression of this kind ...
152 views

A question on JordanDecomposition in Mathematica

How can I have Mathematica show me also the inverse matrix of the similarity matrix of JordanDecomposition of a matrix? Obviously I need to use here the ...
143 views

How do I invert a function with two arguments? [closed]

I begin with a function defined by c[u_, mH_] I won't go into details because it comes from countless lines of partial differential equations, boundary ...
133 views

InverseFourierTransform very slow

I determined a distribution dist = SmoothKernelDistribution[ListOfValues];. Then I determined the FT of the PDF, which is the ...
12k views

How do I get the inverse of a homogeneous transformation matrix?

I want to get the inverse of this homogeneous transformation matrix: iab = { {1, 0, 0, 0}, {0, 0, -1, 0}, {0, 1, 0, 3}, {0, 0, 0, 1} } using the ...
464 views

How to tell Mathematica to get the real-only inverse function?

The problem I have is that Mathematica seems to play better with complex numbers so that the result of N[InverseFunction[Function[x,x^3]][-1]] is ...
114 views

How to find selected elements of inverse of a banded matrix without inverting it?

Is it possible to find some selected elements of the inverse of a large sparse matrix without inverting it? For example consider this Hermitian matrix (as a general case). ...
227 views

Back from transfer function (s-domain) to differential equation (in t-domain)

I've got the following transfer function (in the s-domain): $$\text{H}(s)=\frac{\text{C}s}{\text{RC}s+1}$$ Is there a function in Mathematica 10 that I can go back to the differential equation (in ...
68 views

Evaluation of InverseFunction at the boundaries of its domain

Folks, I want to numerically evaluate a InverseFunction h[x] close to the edges x5 and <...
139 views

Replace variable with # and pass function body as an argument to a function

I have a very simple problem, which I would like to make a bit general, but none of my naive approaches have worked yet. This is what I want to do step by step: Define a parameter: ...
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: ...
79 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: ...
71 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)(...
57 views

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

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

Inverse of a Digamma/ Polygamma Function

How one can find the inverse of a digamma/ Polygamma function in Mathematica 10?
302 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 ...
393 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 ...
28 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 ...
214 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: ...
902 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: ...
101 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): ...
75 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: ...
600 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 ...
519 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: ...
386 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 ...
64 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 ...
614 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 $M=A M^{\dagger} A$ ...
1k 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 ...
201 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 ...
373 views

290 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)
378 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 \$\,\,\,\...
230 views

Inverse functions - how are they calculated?

Mathematica is able to calculate InverseFunction[LogIntegral] and InverseFunction[RiemannR] (and many other inverse functions). ...
833 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 ...
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 ...
376 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 ...