# 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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### Inverse calculation

I am trying to project estimated internal resistance of a battery. We know that the internal resistance approximately halves as the capacity of the battery doubles. For example... A 2AmpHour cell ...
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### Sherman-Morrison formula and a sum of outer products

A specific form of the general Sherman-Morrison formula reads $(1+u v^T)^{-1}$ = $1 - \frac{u v^T}{1+v^T u}$ where $1$ is the identity matrix, $u,v$ are vectors (say with length n) and T denotes ...
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### Classifying functions whose inverse do not have a closed form

My initial question contained about how to classify functions whose integrals and inverses do not have a closed form. But I found this question: How can you prove that a function has no closed form ...
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### Finding modular inverse (wrong approach)

I'm trying to find the modular inverse of $$30 \pmod{7}$$ I have tried using the Euclidean algorithm and it gave me the right answer, which is $x \equiv 6 \pmod{7}$. However, I tried using another ...
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### Easy way to find an inverse in $Z_n$

Well, I'm solving for x in $11x=3$ in $Z_{12}$. And the way for me to do this is finding the inverse of 11 in $Z_{12}$. But to get the inverse, I've tried all possible elements in $Z_{12}$ so that ...
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### Solving $3\times 3$ matrix equations:

I am familiar with finding the inverse of matrices, but struggle to formulate matrix equations. In this particular question, one is asked to find the elementary matrix E where $E*A = B$. $A$ is ...
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### sum of matrix inverse problem

Recently, when I was reading matrix analysis, a formula confused me a lot: If $A+B$ is nonsingular, then the following is true, $$A(A + B)^{-1}B = B(A + B)^{-1}A$$ I tested some random ...
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### Logarithmic to linear

Given this function: $$\frac{1.0}{1024.0} + \frac{x}{100.0} * \frac{1023.0}{1024.0} = y$$ $$10 * \frac{\log_{10}(y)}{\log_{10}(2)} = z$$ $$z * 100 = a$$ ...
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### What kind of distribution in this chart?

Could you tell me what kind of distribution is this? Chart This is the data: ...
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### Relationship between inverse of related matrices

Suppose I have a matrix $A \in \mathbb{R}^{m\times n}$ with $m \geq n$ and suppose that a matrix $G=(A^T A)^{-1}$ exists. Now suppose that I have an other matrix $B \in \mathbb{R}^{m\times m}$ that ...
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### Is this system invertible?

$y(t) = \int\limits_{-\infty}^{\infty} \frac {x(t)^2}{x(t-1)} dt\\$ I was trying to prove or disprove the invertibility of this function. The only thing I could think of was differentiating it. But ...
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### Confusion regarding logic in paper, “A NOTE ON THE INVERSION OF POWER SERIES,” published in the AMS journal

I was reading "A NOTE ON THE INVERSION OF POWER SERIES" and was able to follow the paper's reasoning until the bottom of the second page, where it states: in fact we can calculate the power series ...
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### Trace of Hermitian Positive Semidefinite Matrix

Well, the question I want to ask is as follows. Suppose A and B are Hermitian Positive Semidefinite (PSD) matrices, I wonder if it is possible to prove $Tr(A*(A+B)^{-1})\in (0,1]$ (if it is correct)?...
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### Necessary and/or sufficient conditions for $A+B$ to be invertible

Let $A$ and $B$ be two $n\times n$ real invertible matrices. Are there necessary and/or sufficient conditions (involving only $A$ and $B$ separately, not $(A+B)$ iteself) for $A+B$ to be invertible? ...
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### Inverse of the Cross Ratio for Mobius Transformation from Circle to Circle

I'm reading Conway's complex functions of one variable, and in chapter 3 he goes over Cross-Ratios. He defines the cross ratio to be $(z,z_1,z_2,z_3)=\frac{(z-z_3)(z_2-z_4)}{(z-z_4)(z_2-z_3)}$, where ...
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### What does it mean for f([x])=[2x] for a function mapping R/Z to R/Z?

Let X=R/Z (the circle), with a map $f : X → X$ given by $f([x]) = [2x]$. I'm a little lost on what $f([x]) = [2x]$ means. I thought the function was mapping the equivalence class [x] to the ...
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### Linear Algebra - Real Matrix and Invertibility [closed]

Let $M=\begin{pmatrix}A&B\\C&D\end{pmatrix}$ be a real matrix $2n\times 2n$ with $A,B,C,D$ real matrices $n\times n$ that are commutative to each other. Show that $M$ is invertible if and only ...
Given $M$ is an invertible matrix, and {$\vec{v_1}...\vec{v_k}$} spans $R^n$, then {A$\vec{v_1}...A\vec{v_k}$} also spans $R^n$ What does matrix invertibility have to do with span?