# 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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### Find the inverse of $θ:P(\Bbb{Z})→P(\Bbb{Z})$ defined as $θ(X) = \bar X$

Find the inverse of $θ:P(\Bbb{Z})→P(\Bbb{Z})$ defined as $θ(X) = \bar X$ (the complement of $X$)? Would the inverse of the function just be the function itself?
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### Changed codomain of inverse trigonometric functions

If codomain of $\arcsin(x)$ is $(\pi/2 , 3\pi/2)$ and codomain of $\arccos(x)$ is $(\pi , 2\pi)$ then what should be $\arcsin + \arccos$ equal to ? I thought of putting $x = \sin \theta$ But then ...
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### Inverse of a “Vandermonde-like” matrix composed of power series

Is there an analytical formula for the inverse of a complex matrix whose elements are sets of "power series" except the last term is scaled? Let $0<x_1<x_2<...<x_n$ be monotonically ...
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### Inverse function to $f(t)=3t+4ln(t+1)=y$

I have to invert the function $f(t)=3t+4\ln(t+1)=y$, so $f^{-1}(y)=t$. But I am struggling to invert this. Is there a solution?
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### Prove $sgn(π) = sgn(π^{-1})$?

I'm pretty sure the inversion count of $π$ should be the opposite of the inversion count of $π^{-1}$. By this I mean if $π$ looks like this: $1 \to 1$, $2\to 2, \ldots, 10 \to 10$ and therefore the ...
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### Is the inverse of a real, continuous “1-1” function necessarily continuous itself? [closed]

If so, please do provide me with an epsilon-delta proof, if possible. Thanks in advance.
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### Inverse of the sum of a invertible matrix with known Cholesky-decomposion and diagonal matrix

I want to ask a question about invertible matrix. Suppose there is a $n\times n$ symmetric and invertible matrix $M$, and we know its Cholesky decomposion as $M=LL'$. Then do we have an efficient way ...
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### Question involving inequalities of greatest integer function of inverse trigo.

My question: Find the solution set of $$\lfloor sin^{-1}(x)\rfloor>\lfloor cos^{-1}(x)\rfloor$$ Can anyone help me to solve this question? Graphically it seems to be more complicated.
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### Is a regular stochastic matrix definitely nonsingular?

Is a regular stochastic matrix definitely nonsingular (invertible)? How to prove it ? It says here that 'For a regular matrix always an inverse matrix exists' http://www.vias.org/tmdatanaleng/...
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### Inverse Trig Functions Composite functions of Csc, Sec, And Cot

Ok guys.. I'm trying to get prepared for my test tomorrow and I did numerous exercises. But I stumbled upon one of the "types" of exercises. Which is a composite function in $\csc$ and $\sec$. For ...
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### Matlab function for finding matrix inverse with cayley hamilton theory

I want to write function in matlab that would calculate the inverse of a matrix using its trace. I know that there are other ways to calculate the inverse but I need it to be with trace. I couldn't ...
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Consider, for $\sigma^2_u, \sigma^2_e > 0$, the matrix $$\mathbf{X} = \begin{bmatrix} \sigma^2_u+\sigma^2_e & & & \\ & \sigma^2_u+\sigma^2_e\ \\ & & \sigma^2_u+\sigma^2_e &... 1answer 47 views ### Inverse Fourier transforms with Heaviside step function I want to find the inverse Fourier transforms of:$$u(\nu + 1) \ \exp(-\nu)$$Attempt: So the inverse Fourier transform is given by:$$\int^\infty_{-\infty} u(\nu + 1) \ e^{-\nu} e^{j2 \pi t} \ d\...
Whats the $$\int (\cos(\tan^{-1}(\sin(\cot^{-1}x))))^2dx$$ no idea what to substitute already this is looking bad and that square is making things worse. Please help Thanks!!
Find the inverse Fourier transform of the following: $$\sin(2 \pi \nu T) \cos (10 \pi \nu T) / (\nu T)$$ Attempt: I was told it was easier if we rewrite this in terms of a $sinc$ function. I think ...