# 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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### Solving $\det{(A+\epsilon B)}=0$ for large, symmetric and dense $A$ and $B$

In an algorithm I am writing, I need to solve the equation $$\det{(A+\epsilon B)} = 0,$$ for the smallest value of $\epsilon$, given large ($n$x$n$ ideally up to 150x150), dense and symmetric A ...
3answers
1k views

### What are the counterparts in Wolfram to left and right division of a matrix in other programming language, e.g. Julia and MATLAB?

Sometimes, to find the inverse of a matrix is a labor-consuming task, or even "disgusting", especially when the matrix is "ill". It is said, e.g. in Julia, that the left/right division operation is ...
1answer
77 views

### InverseFunction's domain is not the range of the function that was inverted

I wrote a function to calculate how long of a period has past when a planet traverses an angle theta from perihelion in an orbit of a given eccentricity. ...
3answers
604 views

### Can I use Compile to speed up InverseCDF?

I'm repeatedly issuing the command P = InverseCDF[NormalDistribution[0, 1], T] where T is either a 36- or 64-vector of real numbers (points in the unit ...
0answers
33 views

### Inverse of Normal Distribution CDF incorrect for large value?

I have a function F which is the CDF of the standard normal distribution. The inverse of F should be infinity at 1. However, I ...
1answer
140 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)...
1answer
67 views

1answer
135 views

### Finding the inverse function of an interpolating function given by NDSolve

Consider the following solution of NDSolve ...
3answers
326 views

### Easiest way to have an approximation of binary entropy inverse

I call $H_2$ the function $H_2(x) = -x \ln(x)-(1-x) \ln(1-x)$ It is the binary entropy. I call $g(x)=H_2((1+x)/2)$ This last function is bijective on $[0;1]$. I would like to have an inverse, or ...
0answers
76 views

### Fast method for getting the inverse function of the Hypergeometric function in Mathematica

I didn't manage to obtain the inverse function for this frightening function: ...
1answer
176 views

### Inverse of a multivalued function

I try to get the inverse of a simple function like x^2,x≥0. Still, when I use InverseFunction Mathematica gives me back -(y^0.5) ...
1answer
130 views

### Is there a fast way to get the diagonal of the inverse of a banded Hermitian matrix?

Since inverting a matrix is often a bad idea, I am wondering if there is a better way to get just the diagonal of the inverse without inverting the whole thing. Note I need the whole diagonal, not the ...
1answer
852 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 ...
1answer
385 views