Articles of reference request

Recommended Reading on Regression Analysis?

For a university project, I am implementing an automated regression analysis tool. However, I have very little background in statistics. So what books / articles / material would you suggest I could use to brush up on this topic, based on your experiences? Thanks

Looking for a reference to a proof of $(I – A)^{-1} = I + A + A^2 + A^3 + \ldots$

On some online forum, there is the claim: Given some square matrix: $$(I – A)^{-1} = I + A + A^2 + A^3 + \ldots$$ This is true if the right side converges, which is true if and only if all of the eigenvalues of A have absolute value smaller than $1$. Reference https://www.physicsforums.com/threads/matrix-inverse-equals-power-series.423897/ I […]

Models of hyperbolic geometry

Wikipedia states the following: [The Poincaré half-plane model of hyperbolic geometry] is named after Henri Poincaré, but originated with Eugenio Beltrami, who used it, along with the Klein model and the Poincaré disk model (due to Riemann) But it doesn’t give any sources. I would like to know about the real history of the models […]

Is there a complex variant of Möbius' function?

When you’re dealing with arithmetic functions, you might have come across the classical Möbius’ function $$ \mu(n)=\begin{cases} (-1)^{\omega(n)}=(-1)^{\Omega(n)} &\mbox{if }\; \omega(n) = \Omega(n)\\ 0&\mbox{if }\;\omega(n) < \Omega(n).\end{cases}, $$ where $ω(n)$ is the number of distinct primes dividing the number $n$ and $Ω(n)$ is the number of prime factors of $n$, counted with multiplicities. Is there […]

Paracompact image of an open continuous map from a Čech-complete space

Theorem: Assume that $X$ is Čech-complete, and $Y$ is paracompact. If there exists $f\colon X\to Y$ which is surjective, open and continuous then $Y$ is Čech-complete. The theorem appears as a corollary in a paper by Michael [1] where he proves a much stronger theorem. In the same paper he refers to papers by Pasynkov [2] and […]

A question on generalization of the concept of derivative

I am looking for some material to understand the process of generalization of the concept of derivative. I would not like to just read and apply the definition of the concept of differentiation in order to comprehend this generalization. I would like to work with Differential Calculus fluently so please forgive me if this is […]

Is finding the length of the shortest addition chain for a number $n$ really $NP$-hard?

I spent a few hours today working through the addition chain problem. Given the starting number 1, how many additions are required to get to some target natural number n? For example, to make 5, we need three additions: 1 + 1 = 2 2 + 2 = 4 4 + 1 = 5 To […]

Prerequisites for Linear Algebra Done Right by Sheldon Axler.

I’ve read some notes online and I learned so far: $\{\overset{\displaystyle\ldots}\ldots$ Systems of Two Linear Equations $\rlap{\require{cancel}{\rlap{\Huge\times}\cancel{\color{white}h}}}{\begin{bmatrix}\quad\end{bmatrix}}\,\,$ Gaussian Elimination $\left[\vdots\,\vdots\,\vdots\right]$ Matrices $(\square^{-1})$ The Inverse of a Square Matrix (and also how to solve $\sf Ax=B$) $\left|\,\overset{\overset{\displaystyle\cdot}{}}.\,\overset{\overset{\displaystyle\cdot}{}}.\right|$ Determinants and Cramer’s Rule Is this enough to start reading the celebrated book Linear Algebra Done Right by the […]

Looking for a Resource to Identify/Name a Given Graph

Sometimes specific graphs have very nice properties and tend to pop up often enough that they have been given names like the Petersen Graph, the Rook’s Graph, the Durer Graph, etc. Is there any convenient way to “look up” a graph without first knowing its name in order to find out if it has a […]

Technique for proving four given points to be concyclic?

While making my way through an exercise, I stalled on question 7: 7. Prove that the points $(9, 6)$, $(4, -4)$, $(1, -2)$, $(0, 0)$ are concyclic. The book does not provide any guidance on how to tackle such a question and I can only assume that the authors are assuming that anybody using their […]