8:09 AM
> The tag matrix-inverse (6 questions) seems overly specific and in my opinion it should be removed outright.
The tag grown 59 questions since then. Since several tags were mentioned in that post, it is not clear whether we can count the upvotes there as a support for removal of this particular tag.
However, there is another post about .
5

This suggestion came from an edit I am reviewing, by user Tommi Brander. The tag inverse is currently used for a mismatch of different questions and is not helpful at all. Most of these questions involve matrix inverses: they are a basic concept, but do they deserve their own tag as opposed to li...

The tag currently has 16 questions. After a quick look I'd say that:
In these questions it is used in the sense of inverse matrix, so probably they can be retagged with .
2

$\newcommand{\tr}{\operatorname{tr}}$Does submodularity property hold for the trace of a positive-definite hermitian matrix? I.e., does given any real symmetric positive-definite matrices $X,A,B$ $$\tr X^{-1} + \tr(X+A+B)^{-1} \geq \tr(X+A)^{-1} + \tr(X+B)^{-1}$$ hold? UPD: I have checked it...

1

Consider the following feasibility problem: Find an $n \times n$ stochastic matrix $L$ such that $L^{-1} M L x$ is a non-negative vector, where $M$ is a known $n \times n$ positive matrix and $x$ is an $n$-dimensional probability vector (i.e., elements of $x$ add to $1$ and are non-negative)....

Here the tag is used for inverse transform.
1

I have the following problem. If i can get some help, I would greatly appreciate it. I am trying to replicate a particular research paper and came across a problem: Suppose X is a birth death process (represents population size) that evolves by: $X -> X+1$ if a birth occurs with rate $\mu$ ...

2

We have a 2D order-2 polynomial, a Gaussian and a 'box' indicator function. Let: $\begin{eqnarray} p(x,y) &=& c_0+c_1x+c_2y+c_3xy+c_4x^2+c_5y^2+c_6xy^2 \\ G(x,y) &=& c_k\cdot\exp\left(\frac{-(x^2+y^2)}{2\sigma^2}\right) \\ \square_a(x,y) &=& \mathbf{1}_{[-a,a]\times[-a,a]}(x,y) ... 3 I am looking for the associated inverse kernel to the integral transform$T$defined by$(Tf)(u) = \int_{-\infty}^{+\infty} K(u,t)f(t) \ dt,\ \ u \in \mathbb{R^+}$whose kernel is$K(u,t) = \frac{2cu}{c^2u^2+4\pi^2(u-t)^2}$for a given$c > 0$. Edit: this other form of the integral transform ... And in the most questions it is used - as far as I can tell - for inverse function: -4 Let$C(\mathbb{R})$be a space of continuous functions, let$f$be a real valued function$\mathbb{R}\to\mathbb{R}$, and let$g$be a continuous and differentiable function such that$g$is invertible and positive. My question here is:$Q_1:$How do I solve this equation:$e^{f(f(x)}={g^...

1

As we know there is the expression (f.g) for unary function composition. Is there any reference containing expression for multivariate function composition? I found the only expression searching by 'function composition' in Wikipedia is: $f|_{x_{i}=g}=f[x_{1},x_{2},\cdots,x_{i-1},g(x_{1},\cdots... 14 Let$f$be a function such that :$f:\mathbb{R}\to \mathbb{R}$and$f^{-1}$is a compositional inverse of$f$. I would'd like to know how do I solve this class of differential equation : $$\displaystyle \ f'= e^{\displaystyle {f}^{-1}}?$$ Note 01:$f' =\displaystyle\frac{df}{dx}$. Edit:$...

1

In mathematics, an inverse function is a function that "reverses" another function: if the function $f$ applied to an input $x$ gives a result of $y$, then applying its inverse function $g$ to $y$ gives the result $x$, and vice versa. i.e., $f(x) = y$ if and only if $g(y) = x$ , i'm interesting t...

13

Liouville's theorem gives such a proof for antiderivatives of functions like $e^x/x$ or $e^{x^2}$, and differential Galois thory extends that to Bessel functions, say. But what tools exist for implicit functions like Lambert's W?

5

My question: Is there an equation connecting the two branches $W_0(y)$ and $W_{-1}(y)$ of the Lambert W function for $y \in (-\tfrac 1e,0)$? For example the two square roots $r_1(y)$ and $r_2(y)$ of the equation $x^2=y$ fulfill the equation $r_1(y)=-r_2(y)$. So if one has computed one root, he a...

6

Let $f:X\to Y$ be a bijective rational map of an open dense subset $X$ of $\mathbb{C}\times\mathbb{C}$ onto an open dense subset $Y$ of $\mathbb{C}\times\mathbb{C}$. How to prove that the inverse map $f^{-1}:Y\to X$ is rational as well? Could you recommend any exact reference to a theorem which g...

2

I am aware of the inverse function theorem for Lipschitz maps, which uses the notion of generalised derivative $δ_{x_0} f$ of a Lipschitz map $f$, due to F.H.Clarke: Teorem. Let $f : U ⊂ \mathbb{R}^n → \mathbb{R}^n$ be Lipschitz, and suppose that every matrix $A ∈ δ_{x_0}f$ is invertible. Then ...

5

I have the series $\sum_{n=0}^{\infty}(-1)^{n}a_{n}(\nu)\frac{\sin[\nu\,(m-n)]}{\nu\,(m^2-n^2)}=\frac{1}{m}$, where $m$ is an integer. Is it possible to compute the coeffients $a_{n}(\nu)$? An exact solution is found for $\nu=\pi$: $a_0=1, a_{n}=2\times(-1)^n$. It is related to a wel...

2

I have been trying to solve the following difference equation for some time now : $$u^3(n+1) = a - b\cdot u^2(n) + u^3(n), \qquad a \ne 0 \ne b$$ I have tried various substitutions, simplifications but nothing did. My last attempt was to transform it into a continuous differential equation by le...

@FrançoisG.Dorais When you have some time to look at tag-related issues - what do you think about removal of tag - as proposed by Federico Poloni‌​.
And if it is going to be removed, will it be done by moderators (=without bumping) or should it be edited away manually?
BTW since I have mentioned also , I will add that this tag at least has tag-excerpt. (In the case of the (inverse) tag, the tag-info is empty.)

9:08 AM
I have also mentioned this to Federico Poloni:
I have tried to summarize the current status on (inverse) tag here in chat. — Martin Sleziak 48 mins ago

9:40 AM
@MartinSleziak: I deleted the inverse tag.

@FrançoisG.Dorais I see you (or somebody) have also deleted the answer about this tag.
Isn't it better to keep past discussion about tags undeleted?
Now if somebody creates tag again (which is not that unlikely), this might lead to new discussion on meta about the same tag.
If the discussion is still accessible, we can simply remove the tag and add link to the previous discussion (as a supporting evidence that there is some consensus on this).
And I should have started by saying thanks for handling the tag.
Of course, I am aware that 10k+ users still can see the discussion even after the deletion. So, in some sense, it is still accessible to some users.