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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23
votes
3answers
3k views

How to symbolically do matrix “Block Inversion”?

Consider a block (partitioned) matrix matrix = ArrayFlatten[{{a, b}, {c, d}}] where, a, ...
1
vote
1answer
464 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 ...
6
votes
2answers
2k views

How to invert an integral equation

There have been numerous times when I've needed to invert an integral equation, i.e. I have something like $$f(x) = g_1(x)\int_{0}^x g_2(x') dx'$$ for arbitrary functions $g_1$ and $g_2$, and ...
8
votes
2answers
4k views

Inverse of a complicated function

Mathematica is struggling to find the inverse of this function f(r): ...
3
votes
1answer
527 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 ...
3
votes
2answers
4k 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) : ...
3
votes
3answers
825 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 ...
9
votes
2answers
472 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}}] ...
5
votes
1answer
215 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 ; ...
3
votes
3answers
1k views

Changing variables algebraically

Suppose one has two functions, $y(x)$ and $z(x)$, and one seeks to obtain $y(z)$ by substituting $x(z)$ into $y(x)$. Can this be done in a single step? Or must $z(x)$ first be inverted independently? ...
-3
votes
2answers
62 views

Inverse of function including hyperbolic cotangent [closed]

How can I create a numeric function for the inverse of $y(z) =\coth{z}-\frac{1}{z}$, over the range of $y\in [0, 1]$ and $z\in [0, \infty]$?