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eklausmeier.goip.de | ||
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nhigham.com
For a polynomial $latex \notag \phi(t) = a_kt^k + \cdots + a_1t + a_0, $ where $latex a_k\in\mathbb{C}$ for all $latex k$, the matrix polynomial obtained by evaluating $latex \phi$ at $latex A\in\mathbb{C}^{n \times n}$ is $latex \notag \phi(A) = a_kA^k + \cdots + a_1A + a_0 I. $ (Note that the constant term is... |
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mkatkov.wordpress.com
For probability space $latex (\Omega, \mathcal{F}, \mathbb{P})$ with $latex A \in \mathcal{F}$ the indicator random variable $latex {\bf 1}_A : \Omega \rightarrow \mathbb{R} = \left\{ \begin{array}{cc} 1, & \omega \in A \\ 0, & \omega \notin A \end{array} \right.$ Than expected value of the indicator variable is the probability of the event $latex \omega \in... |
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www.jeremykun.com
This proof assumes knowledge of complex analysis, specifically the notions of analytic functions and Liouville's Theorem (which we will state below). The fundamental theorem of algebra has quite a few number of proofs (enough to fill a book!). In fact, it seems a new tool in mathematics can prove its worth by being able to prove the fundamental theorem in a different way. This series of proofs of the fundamental theorem also highlights how in mathematics there are many many ways to prove a single theorem... |
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ianwrightsite.wordpress.com
Riemann's Zeta function is an infinite sublation of Hegelian integers. |
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