# Tagged Questions

Inverses include: multiplicative inverse of a number (reciprocal), inverse function, matrix inverse, etc. A subject tag such as (linear-algebra), (algebra-precalculus) or (arithmetic) should be added to clarify in which sense "inverse" is used. This tag should never be the only tag on a question.

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### a practical question about matrix derivative with inverse and chain rule: dimension mismatch

Recently, I was trying to take the following derivative $$\dfrac{\partial (X^TV^{-1}X)^{-1}}{\partial V}$$ I was referring to matrix cookbook to solve it, where I found several useful equations: ...
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### Why does Arccos(Sin(x)) look like this??

I can kind of understand the main direction (slope) of $y$ over the different $x$ intervals, but I can't figure out why the values of $y$ take on the shape of straight lines and not curves looking ...
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### Consider $f : \mathbb{N} → \mathbb{Z}$ defined as $f (n) = \frac{(−1)^n (2n−1)+1}{4}$. Find its inverse.

I cannot find an inverse of this function for $f(n) = x$, where $x$ is an integer, that gives out a natural number. Some guidance would be very helpful... I already know the function is bijective so ...
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### Hessian for inverse probit link

I'm trying to calculate Hessian and Fisher Information for binomial model using inverse probit link, Suppose likelihood function is $L(\pi)=\prod\limits_{i=1}^n \pi_i^{y_i}(1-\pi_i)^{1-y_i}$ and ...
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### Inverse of function - Difficulty solving [closed]

$$y=\sqrt{35\tan (\frac{\pi }{180}x)}$$ I have a really hard time finding the inverse of this particular function. Can anyone shine some light on why that may be, or alternatively solve it if I'm ...
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### Proving a matrix is invertible

There's a linear algebra problem I'm having some trouble with: Let $A$ and $B$ be square matrices with the dimensions $n\times n$. Prove or disprove: If $A^2 + BA$ is invertible, then $A$ is also ...
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### Are these equiv? $\cot^{-1}(-x) = -\cot^{-1}(x)$

$-\cot(y)=x$ Let's say you want to put this in terms of y... $\cot(y)=-x$ $y = \cot^{-1}(-x)$ =================== Is this also valid ? $-\cot(y)=x$ $y = -\cot^{-1}(x)$ If yes, how exactly does ...
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### If the product of two square matrices is invertible, then both matrices are invertible

If $A$ and $B$ are $n\times n$ matrices, and $AB$ is invertible then $A$ and $B$ are invertible. I started out by writing that since $AB$ is invertible, then for the equation $ABx=b$ has a unique ...
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### If f(x+y)=f(x)*f(y) and f is a bijection, show that its inverse satisfies this function equation

I'm having trouble with this problem. I'm not even sure how to go about finding the inverse of an equation with both x and y. Here is the problem: If $f(x+y)=f(x)*f(y)$ and $f$ is a bijection, show ...
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I have $n$ functions with power series representation as $F_i(X)=\sum_{k_1,\dots k_m}a^{i}_{k_1,k_2,\dots k_m}x_1^{k_1}x_2^{k_2}\dots x_n^{k_n}$, where $X=[x_1,x_2,\dots,x_n]$ and $F(x)=[F_1(X),\dots,... 0answers 16 views ### How can I calculate the inverse fourier transform of$jw$I am trying to solve$h_I(t)$, which is satisfying$h(t)*h_I(t)=\delta(t)$. e.g. If$h(t) = \delta(t+c)$, then$h_I(t)=\delta(t-c)$. If$h(t) = u(t)$, then$h_I(t)=\delta'(t)$. Q) What is the ... 1answer 23 views ### How do I Inverse Laplace$\frac{(s+1)^3}{s^4}$I missed a class this week in maths and been a bit lost since with Inverse Laplace, how do I go about finding the Inverse laplace of: $$\frac{(s+1)^3}{s^4}$$ Do I simply expand the numerator? then ... 0answers 30 views ### Use conformal mapping to get a heart shape from a square I use what I call "inverse" conformal mapping in order to properly handle integer locations of output pixels. In other words, if z = x + iy = (x, y) is an output pixel, then I use f(z) = (X + iY) ... 1answer 46 views ### Polynomial modular inverse I am trying to understand the modular inverse of a polynomial. Let$A , Q$be polynomials; what is the polynomial$B$such that$A B = 1 \pmod Q$? I tried searching articles from Finding inverse of ... 2answers 70 views ### Given that$ A$is a square matrix such that$ A^2 -4A -3I =0$how do I find$(A+2I)^{-1}$The way I tried to solve this is to find out how much$(A+2I)$equals then find it's inverse so: $$A^2 -4A -3I == A^2 -3A-A -2I-I=0$$ $$A^2 -3A-I = (A+2I)$$ Do I simply just inverte the left ... 1answer 21 views ### matrix algebra with invertibles Im asked to solve for X given the equation $$(A^{-1}X)^{-1} = (AB^{-1})^{-1}(AB^2)$$ What I have done so far is: $$((A^{-1}X)^{-1})^{-1} = ((AB^{-1})^{-1}(AB^2))^{-1} \\A^{-1}X = ((AB^{-1})^{-1}(AB^... 4answers 47 views ### Inverse function of f(x) = \frac{x+5}{x-2} Find the inverse of the function f(x) = \frac{x+5}{x-2} Here's what I have so far: y = \frac{x+5}{x-2} x = \frac{y+5}{y-2} (x)(y-2) = (y+5) but this seems to be a dead end. How should I ... 0answers 29 views ### inverse square root of band matrix this is my first post in this web site and I hope that I find an answer to my question. I am trying to find a closed-form expression for the inverse square root of the following symmetric band matrix ... 3answers 139 views ### What is the inverse function of e^x +x? As the natural \log(x) function is the inverse of the exponential e^x and \log(x +1) is the inverse of e^x - 1, what it the inverse of e^x + x? 2answers 123 views ### what does it mean for the transpose of a matrix to be the negative of the matrix? Say I have matrix A, if the transpose of A is equal to A then A is symmetrical. but what does it mean if the transpose of A = -A and can I know something about such a matrix inverse? 1answer 29 views ### I'd like to know the inverse of this function: y = 100x + 5 (x - 1) (x / 2) I'm developing a game with a ranking system and I'm using the formula$$y = 100x + 5 (x - 1) (x / 2)$$to figure out how much XP is needed to obtain a certain rank. Now the problem is, I also need to ... 0answers 10 views ### inverse and unitary invariance I want to simplify the expression (\mathbf{V}^H \mathbf{X} \mathbf{V} )^{-1}, where V \in \mathbb{C}^{M\times d}, M>d is unitary but not square, i.e., \mathbf{V}^H\mathbf{V}=\mathbf{I}_d but ... 0answers 43 views ### Consider the relation … What are the domain and range of R? Define the inverse relation. What are its domain and range? Consider the relation R={(x,y)∈ℝ×ℝ:y=2x}. What are the domain and range of R? Define the inverse relation. What are its domain and range? So I was thinking since there is no set given that it would ... 2answers 39 views ### Inversion of a Block Matrix Let S to be a symmetric and positive semi-definite matrix of size n. What is the inverse of the following block matrix$$ M_{2n\times 2n}= \begin{bmatrix} aI+S & -I\\ -I & aI+S \end{... 2answers 95 views ### How to find the range of$1 / (1+x^2)^{1/2}\$?

How to find the range of $$\frac{1}{\sqrt{1+x^2}}$$? Ok. I've revised the (easy theory). I would like to complete the exercise finding the derivative of f(x) and setting equal to zero. I do it ...
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