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Number of self-inverses in a group

An element of order $2$ in a group is often called an involution. In geometric groups reflections are involutions, as are half turns and central involutions, for example. Involutions are normally ...
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Is there a name for the opposite of (vector) projection?

This is called vector rejection. A common concept in Geometric algebra.
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Inverse Trig Identity Proof under different conditions

The identity in your book only holds for when $x > 0, y > 0$: else $\arctan x + \arctan y =$ $\arctan \left(\frac{x+y}{1-xy} \right) - \pi$ instead where $x < 0$ and $y < 0$ (the two cases ...
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Finding Left and Right Inverses

This question is a bit more tricky than you'd think at first glance, like the comments alreads mention that there is no neutral element. And also the operation is not associative. So what's the ...
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Some questions about the pseudoinverse of a matrix

Regarding the first question: Let $\mathbb F$ be a field (not necessarily $\mathbb R$ or $\mathbb C$), and let $m,n$ be nonnegative integers. Given an involutory field automorphism $a:\mathbb F\to\...
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How to compute inverse of this matrix

The Sherman-Morrison formula says that whenever $A$ is an invertible square matrix of size $n$ and $u,v\in \Bbb R^n$ are column vectors such that $1+v^\top A^{-1}u\neq 0$, then $A+uv^\top$ is ...
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A question about sherman–morrison formula

Starting from what you have shown, $$ (A - uv')^{-1} = A^{-1} + \frac{A^{-1} uv' A^{-1}}{1 - u' A^{-1} v} , $$ just multiply both sides by $u'$ and $v$ on the left and right respectively to get what ...
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Inverse of a tridiagonal matrix with all entries unity.

Here is an answer inspired (in particular) by the answer by Calvin Lin to this question. Let us give the indexed name $A_n$ in the case $A$ is $n \times n$. Let $D_n$ denote its determinant. We have ...

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